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w.MV»r>ity    of   California 

IRVfNE 


EX         L   I    B  R 

CASSIUS      MILTON 


I   S 

JAY 


924 


CONTRIBUTIONS  FROM  THE  LICK  OBSERVATORY  NO.  3. 


TERRESTRIAL 


ATMOSPHERIC  ABSORPTION 


PHOTOGRAPHIC  BAYS  OF  LIGHT. 


BY 

J.  M.  SCHAEBERLE, 

Astronomer  in  the  Lick  Observatory. 


Printed  by  authority  of  the  Regents  of  the  University  of  California. 


SACRAMENTO: 

STATE    OFFICE,    :     :     :    A.    J.    JOHNSTON,    SUPT.    STATE    PRINTING. 

1893. 


ORGANIZATION  OF  THE  LICK  OBSERVATORY 


Hon.  T.  G.  PHELPS,  Hon.  C.  F.  CROCKER,  Hon.  H.  S.  FOOTE, 

Committee  of  the  Regents  on  the  Lick  Observatory. 


MARTIN  KELLOGG, 
EDWARD  S.  HOLDEN, 
J.  M.  SCHAEBERLE, 
E.  E.  BARNARD, 
W.  W.  CAMPBELL, 
ALLEN  L.  COLTON 
0.  D.  PERRINE 


President  of  the  University. 

Director  and  Astronomer. 

Astronomer. 

Astronomer. 

Astronomer. 

Assistant  Astronomer. 

.    .......     Secrft>i,->/. 


H 
i 

TABLE  OF  CONTENTS. 


Page. 
Determination  of  the  Relation  between  the  Aperture,  the  Diameter  of  the 

Star  Image,  and  the  Exposure-Time 2 

'  Determination  of  the  Instrumental  Constants 4 

jj  Exposures  on  Polaris  with  the  Great  Telescope,  and  Comparison  with 

Theory.  Table  I 9 

Tabular  values  of  Q,  m',  d,  and  t.  Table  II -  10 

Atmospheric  Absorption  of  the  Photographic  Rays  of  Light 15 

Method  of  Observing 16 

Method  of  Derivation  of  the  Fundamental  Equation 17 

First  Series  of  Observations  (Mt.  Hamilton) 18 

Second  Series  of  Observations  (Cayenne) , 28 

Third  Series  of  Observations  (Mt.  Hamilton) .38 

Fourth  Series  of  Observations  (Mt.  Hamilton) 72 

Final  results  based  on  all  the  Observations 84 

The  Law  of  Photographic  Atmospheric  Absorption.  Equation  (181) 85 

Table  LIX,  giving  the  absorption  in  magnitudes  for  each  degree  of  Z.-D...  86 

The  Probable  Error  of  a  Photographic  Magnitude -  87 

New  Units  of  Brightness  and  Magnitude 87 

Conclusion  ___ 88 

Works  Issued  by  the  Lick  Observatory .  90 


TERRESTRIAL  ATMOSPHERIC  ABSORPTION   OF  THE 
PHOTOGRAPHIC  RAYS  OF  LIGHT. 

By  J.   M.   SCHABBEELK. 


The  remarkable  revolution  in  the  methods  of  charting 
celestial  configurations,  brought  about  by  substituting  <|br)  the 
photographic  plate,  the  human  eye,  has  opened  up  a  most 
inviting  field  of  investigation.  To  obtain  results  which  here- 
tofore demanded  months  and  years  of  labor  on  the  part  of 
the  observer  only  a  few  hours  are  now  required. 

As  a  necessary  consequence  of  this  radical  change  in  the 
methods  of  work  many  new  problems  confront  the  astronomer, 
some  of  which  must  be  solved  before  the  information  given  by 
the  photographs  can  be  presented  in  its  final  form. 

The  human  eye  as  normally  constituted  is  most  sensitive  to 
a  particular  set  of  light  rays.  If  now  we  could  construct  a 
photographic  plate,  on  which  the  set  of  rays  which  are  most 
effective  visually  would  also  be  most  effective  photographically, 
it  is  probable  that  the  relative  brightness  determined  photo- 
graphically would  not  differ  from  that  deduced  from  direct 
visual  observation. 

Up  to  the  present  time;  however,  the  plates  which  have  been 
universally  employed  in  photographic  work  are  so  prepared 
that  the  action  of  the  light  from  near  the  red  end  of  the 
solar  spectrum — or  where  the  light  is  most  effective  visually — 
is  very  much  less  effective  than  that  coming  from  near  the 
violet  end.  For  this  reason  it  would  seem  to  follow  at  once, 
that  whatever  unit  of  brightness  is  chosen,  the  relation  between 
the  visual  brightness  and  that  deduced  from  the  action  of  the 
same  source  of  light  on  the  photographic  plate,  can  only  be 
considered  constant  so  long  as  the  spectral  type  remains  the 
same.  In  general  we  should  expect  that  for  stars  of  different 
types  of  spectra,  the  relation  between  the  visual  magnitudes 
will  not  be  the  same  as  the  relation  between  the  corresponding 
photographic  magnitudes. 

Investigations  relating  to  the  photographic  magnitudes  of 
the  fixed  stars  have  been  made  by  PICKERING,  PRITCHARD, 


2  Terrestrial  Atmospheric  Absorption  of 

CHARLIER,  SCHEINER,  GOULD,  and  others;  a  consideration  of 
the  various  results  seems  to  show  that  the  different  forms  of 
photographic  telescopes  and  plates  do  not,  as  a  rule,  give,  under 
otherwise  similar  conditions,  exactly  the  same  data.  As  will 
be  shown  farther  on,  the  law  deduced  hy  the  present  writer 
holds  good  for  the  three  different  telescopes  available;  two 
being  of  6-inch  aperture,  and  the  third  33-inch.  SEED  plates, 
Sensitometer  No.  26,  were  used  in  all  cases. 

This  line  of  work  was  taken  up  in  1889,  at  the  suggestion  of 
Professor  HOLDEN.  An  equatorially-mounted  DALLMEYER  lens, 
primarily  intended  for  eclipse  work  at  Cayenne,  and  loaned  to 
the  Lick  Observatory  by  the  United  States  Naval  Observatory, 
was  first  employed  for  obtaining  the  necessary  data;  later  on  a 
WILLARD  lens,  belonging  to  the  CROCKER  telescope,  was  also 
used. 

DETERMINATION  OF  THE  RELATION  WHICH,  FOR  A  GIVEN  STAR, 

EXISTS     BETWEEN     THE     APERTURE     (Q)     OF     THE     TELESCOPE 

AND  THE  DIAMETER  (d)  OF  THE  STAR'S  IMAGE  FOR  A  GIVEN 
EXPOSURE  TIME  (t). 

Some  of  the  results  of  a  preliminary  investigation  made  on 
Mount  Hamilton  are  embodied  in  a  paper  entitled,  "  On  the 
Photographic  Magnitudes  of  the  Fixed  Stars."  (See  Publica- 
tions of  the  Astronomical  Society  of  the  Pacific,  Vol.  I,  No.  4.) 

To  obtain  a  general  expression  for  the  brightness  of  a  fixed 
star,  as  determined  by  means  of  its  image  impressed  upon  the 
photographic  plate  during  an  exposure  time  t,  and  with  aper- 
ture D,  I  arranged  the  following  scheme  for  obtaining  the 
necessary  data: 

With  a  known  aperture  of  the  objective,  a  series  of  images 
of  the  star  were  first  obtained,  the  exposure  times  being 
respectively  1s,  2s,  4s,  8s,  16s,  32s,  64s,  and  128s,  the  telescope  being 
slightly  shifted  after  each  exposure  to  keep  the  images  from 
overlapping.  Other  series  of  similar  exposures  on  the  same 
star  and  plate  were  then  made  with  different  known  apertures. 
This  scheme  was  then  applied  to  different  stars. 

Now,  in  the  case  of  any  one  of  these  stars,  the  source  of 
light,  during  the  time  of  one  series  of  exposures,  remains  prac- 
tically constant;  hence,  it  is  evident  that  the  relation  between 
the  exposure  time  t,  the  diameter  of  the  aperture  D,  and  the 


The  Photographic  Rays  of  Light. 


diameter  of  the  star's  image  d,  must  always  be  such  that  the 
expression  for  the  brightness  B  is  a  constant  quantity  for  any 
given  star,  whatever  its  magnitude  may  be. 

From  a  discussion  of  the  data  given  by  these  plates,  I  found 
that  the  law  governing  the  size  and  rate  of  growth  of  the 
image  could  be  expressed  by  means  of  an  equation  of  the  form,* 

d  =  a  +  ft  log  D  +  y  D  log  *.  (1) 

In  which  d  is  the  measured  diameter  of  the  image  for  the 
aperture  D  and  exposure  time  t,  while  or,  /?,  and  y  are  constants 
which  depend  upon  the  telescope,  the  atmospheric  condition, 
and  the  kind  of  photographic  plate  employed. 

Using  this  theoretical  relation  between  d,  D,  and  t,  I  showed 
that  if  Q  represents  the  theoretical  aperture  which  a  standard 
star  (Polaris)  would  require  to  produce  in  the  time  J,  an  image 
having  the  same  diameter  d  as  that  produced  by  any  star 
with  a  constant  aperture  Q0  (6-inch)  in  the  same  time  f,  the 
equation  which  serves  to  determine  the  magnitude  of  any  star 
whose  image  is  impressed  upon  the  photographic  plate  is  of 
the  following  form: 

d  =  <x  +  /310gQ  +  yQlogt.  (2) 

The  corresponding  photographic  magnitude  m'  is  then  found 
by  means  of  the  expression 

,     ,      log  *  Q2 
-~~ 


k  being  a  constant  which  depends  upon  the  photographic 
magnitude  of  the  standard  star.  If  we  take  Polaris  as  the 
standard  star,  and  assume  for  the  present  (only)  its  apparent 
photographic  magnitude  to  be  2.00  at  the  zenith-distance 
52°  40',  corresponding  to  the  co-latitude  of  the  Lick  Observa- 
tory, equation  (3)  becomes 


,       „ 

— 


(For  illustrative  examples,  see  Publications  of  the  Astronom- 
ical Society  of  the  Pacific,  Vol.  I,  No.  4.) 

*As  I  afterwards  learned,  Professor  PRITCHARD,  Director  of  the  Savilian 
Observatory,  had  previously  also  found  that  d  could  be  expressed  as  a  func- 
tion of  log  t. 


4  Terrestrial  Atmospheric  Absorption  of 

DETERMINATION  OF  THE  INSTRUMENTAL  CONSTANTS. 

I  shall  now  attempt  to  show  that  equation  (2),  when  properly 
interpreted,  is  quite  general  in  its  character,  and  apparently 
applicable  to  similar  telescopes  of  any  aperture  actually  em- 
ployed in  photographic  work. 

Let  us  first  consider  the  case  of  two  similar  telescopes  having 
equal  apertures.  From  a  series  of  experiments  made  with  two 
such  instruments  (one  of  which  was  a  DALLMEYER,  the  other  a 
WILLARD  lens  of  5.9  inches  aperture)  I  found  that  while  the 
growth  of  the  images  during  equal  units  of  time  was  practi- 
cally the  same  for  both  instruments,  there  was  a  small  and 
almost  constant  difference  between  the  dimensions  of  the  images 
for  the  same  value  of  t.  This  difference,  taking  the  DALLMEYER 
telescope  as  the  standard,  might  be  called  the  constant  correc- 
tion of  the  WILLARD  lens. 

In  order,  therefore,  to  render  the  measured  quantities  homo- 
geneous, we  must  first  determine  the  correction  to  be  applied  to 
each  d  of  one  instrument,  in  order  to  reduce  it  to  the  normal 
d  of  a  particular  instrument  taken  as  a  standard. 

In  the  following  notation  let  the  symbols  which  are  not 
primed  refer  to  the  standard  (6-inch  DALLMEYER)  telescope, 
and  let  those  with  the  primes  refer  to  a  companion  telescope 
of  equal  (6-inch)  aperture. 

Let  d0  and  d0'  denote  the  diameters  corresponding  to  the 
exposure  time  t0: 

Let  d  and  d'  denote  the  diameters  corresponding  to  the  ex- 
posure time  f: 

And  for  brevity  let 

a-f/JlogQ=c  (5) 

a'  +  /JlogQ  =  c'  (6) 

Then,  since  the  value  of  Q  is  the  same  for  both  telescopes 
when  the  same  star  is  observed,  we  can  write 

d0  =  c  +  rQlogt0  (7) 

d  =  c  +  rQlog«  (8) 

and 

d0'  =  c+y  Qlog£0  (9) 


The  Photographic  Rays  of  Light. 


from  which  the  expressions  for  Q  become 


0=     _       °  _  nn 

y  (log  «- 


O  —  °  H21 

/(log«  —  logt.) 

Hence,  the  difference  between  the  diameters  of  any  two 
images  of  the  same  star  divided  by  the  difference  between  the 
logarithms  of  the  corresponding  times  of  exposure  is  a  constant 
for  the  same  telescope  and  plate. 

We  must  evidently  have  also 


Now,  although  the  values  of  d  and  d'  in  the  two  telescopes 
may  differ  considerably  for  the  same  value  of  t,  still  experi- 
ment seems  to  prove  that  the  difference  between  the  growths 
(d  —  d0  and  d'  —  d0')  of  the  images  in  two  similar  telescopes  can 
be  treated  as  a  quantity  of  the  second  order,  so  that  we  can 
write 

Y  =  Y  (14) 

If  now  we  make  <0  =  ls,  the  expressions  for  the  value  of  Q 
become 

d-d.  (15) 


the  value  of  y  for  the  DALLMEYER  telescope  and  SEED  26  plates 
being  0.0033. 

It  is  evident  that  a  difference  in  the  development  of  the 
plates  may  have  a  great  effect  upon  the  resulting  values  of  d. 
A  strong  development  will,  as  a  rule,  give  larger  images  than 
a  weak  development,  and  as  the  image  of  a  bright  star  grows 
faster  than  that  of  a  faint  star  the  relative  effect  may  be  most 
marked.  Therefore,  not  only  should  the  plates  be  of  the  same 
degree  of  sensitiveness,  but  the  development  of  these  plates  should 
be  uniformly  the  same. 


6  Terrestrial  Atmospheric  Absorption  of 

Equations  (15)  and  (16)  can  be  considered  as  special  differ- 
entials of  (8)  and  (10),  in  which  the  increments  are  finite. 
For  if  we  differentiate  (8)  and  (10),  regarding  d  and  i  as  vari- 
ables, and  designating  the  differential  by  the  symbol  £7  we 
obtain 

6d  =  yQ-±  (17) 

dd'  =  yQ—  (18) 

from  which  we  have 


which  are  identical  with  (15)  and  (16)  when  finite  incre- 
ments are  employed. 

To  determine  the  value  of  the  constant  correction  to  be  ap- 
plied to  the  data  given  by  the  companion  telescope,  we  first 
find  the  value  of  Q  by  means  of  (16).  With  this  Q  as  an 
argument  we  enter  Table  II,  and  take  out  the  values  of  d  corre- 
sponding to  the  exposure  time  t;  then  since  we  also  have, 
according  to  equations  (7),  (8),  or  (9),  (10),  the  equation 

c  —  c'  =  d  —  d'  (21) 

it  follows  that  each  exposure  on  a  given  star  furnishes  an  inde- 
pendent value  of  the  correction  (c  —  c')  to  be  applied  to  the 
measured  values  of  d'  to  obtain  the  normal  or  tabular  values. 
It  also  follows  that  if  the  empirical  formula  is  correct,  the 
several  independent  values  of  these  corrections  should  agree 
within  the  limits  of  the  errors  of  observation. 

Thus  far  we  have  been  considering  the  problem  of  determin- 
ing, with  the  aid  of  data  given  by  an  assumed  standard  tele- 
scope, the  photographic  magnitude  of  a  star  from  the  data  given 
by  a  second  telescope  having  the  same  aperture  as  the  standard 
instrument.  Let  us  now  consider  the  general  problem  of  find- 
ing the  photographic  magnitude  from  data  given  by  a  telescope 
having  an  aperture  n  Q0  referred  as  before  to  the  system  of 
magnitudes  given  by  the  standard  telescope. 


The  Photographic  Rays  of  Light. 


Now,  for  theoretically  perfect  telescopes,  the  magnitude  M' 
corresponding  to  a  given  d,  t,  and  aperture  n  Qo  can  be  expressed 
by  means  of  the  equation 


M       o  (22) 

0.4 

And  for  the  same  values  of  d  and  t  ,  but  with  the  aperture  Q0, 
the  required  magnitude  (m)  necessary  to  satisfy  the  conditions 
would  be  expressed  by  equation  (4).  The  difference  between 
equations  (4)  and  (22)  for  the  same  t  and  d  will  evidently  be  a 
constant  quantity,  whose  value  is  given  by  the  equation 

M  '  —  m  =  5  log  n  (23) 

or, 

M'  =  m  +  5  log  n  (24) 

Hence,  with  the  aid  of  Table  II  we  should  also  be  able  to 
determine  the  theoretical  photographic  magnitude  of  a  star  pho- 
tographed with  an  aperture  n  Q0  by  simply  adding  5  log  n  to  the 
tabular  m  corresponding  to  the  observed  arguments  d  and  t. 

However,  in  deducing  the  law  expressed  by  equation  (1)  all 
the  imperfections  peculiar  to  the  particular  standard  instru- 
ments are  involved;  that  is,  the  law  is  so  determined  that  the 
constant  corrections  are  already  applied.  But  the  imperfections 
of  another  telescope  will  not  necessarily  be  the  same  as  those 
of  the  standard  instrument,  so  that  generally  the  measured 
values  of  d  will  be  in  error  when  referred  to  the  standard 
instrument.  It  is  therefore  essential  to  use  the  corrected  value 
of  d';  or  to  determine  the  value  of  Q  by  means  of  equation  (12) 
or  (16)  where  the  constant  is  eliminated. 

As  I  very  much  desired  to  learn  how  closely  these  formulae 
represented  the  observations  for  those  cases  in  which  Q0  and 
n  Qo  were  very  different,  the  theory  was  tested  by  means  of  the 
most  extreme  practical  case  which  could  be  applied  at  the  pres- 
ent time.  At  my  request  Professor  HOLDEN,  aided  by  Professor 
CAMPBELL,  made  a  series  of  suitable  exposures  for  me  upon  the 
star  Polaris  with  the  great  refractor,  the  clear  aperture  of  which 
for  photographic  purposes  is  33  inches. 


8  Terrestrial  Atmospheric  Absorption  of 

As  our  unit  of  aperture  is  6.00  inches  we  have  for  substitu 
tion  in  equation  (22)  the  values 

Q.=4=1.00 

^      ' 


The  true  tabular  magnitude  m  is  therefore  according  to 
equation  (24), 

M'  =  m  -f-  5  log  5.5  =  m'  -f  3.70. 

To  compare  this  result  with  actual  observation  we  employ 
equation  (16)  in  order  to  eliminate  the  constant  errors  of  the 
d  (given  in  the  table)  in  determining  the  value  of  Q. 

From  the  observed  data  we  have  for  values  of  t  =  1*  and  t  =• 
256',  the  corresponding  values  d'  =  0.0250  and  d'  =  0.0700; 
hence,  according  to  actual  observations  we  have 

nQ°=5.67  (26) 

Agreeing  fairly  well  with  the  theoretical  value  5.50  found 
above.  The  tabular  magnitude  corresponding  to  n  Q0  =  5.67  is 
—  1.77;  hence,  according  to  equation  (24), 

m  =  3.70  —  1.77=1.93  (27) 

When  it  is  considered  that  this  result  for  the  magnitude  of 
Polaris  (differing  only  Om.07  from  the  adopted  magnitude)  is 
practically  the  same  as  that  given  by  the  6-inch  objective,  it 
would  seem  to  indicate  that  the  results  obtained  with  different 
instruments  are  less  heterogeneous  than  might  naturally  be 
expected,  for  in  the  present  case  not  only  are  the  apertures  very 
different,  but  for  the  33-inch  telescope  the  ratio  of  aperture  to 
focal  length  is  only  about  one  third  as  great  as  it  is  for  the 
DALLMEYER  lens.  Discrepancies  in  the  results  given  by  differ- 
ent observers  are  probably  largely  due  to  the  fact  that  the  con- 
stants peculiar  to  each  instrument  and  plate  have  not  been 
sufficiently  sharply  determined,  and  still  more  largely  due  to 
differences  in  the  degree  of  development  of  the  photographic 
plates. 

To  show  the  practical  agreement  between  theory,  as  defined 
by  equation  (2),  and  observation,  I  give  the  data  obtained  with 
the  great  telescope,  using  all  the  exposures  made  on  Polaris. 


The  Photographic  Rays  of  Light.  9 

In  the  following  table  the  first  column  gives  the  duration  of 
the  exposures;  the  second  column,  the  diameters  of  the  corre- 
sponding stellar  images;  the  third  column,  the  tabular  diameters 
corresponding  to  n  Q  =  5.67,  as  found  by  observation;  the  last 
column  contains  the  individual  values  of  the  constant  correction 
c — c0  to  be  applied  to  all  measured  values  of  d'  to  make  them 
comparable  with  the  values  given  in  Table  II. 

EXPOSURES  ON  POLARIS  WITH  THE  33-iNCH  PHOTOGRAPHIC  TEL- 
ESCOPE, AND  COMPARISON  WITH  THEORY,  FOR  TESTING  THE  LAW 
DEDUCED  FROM  EXPERIMENTS  MADE  WITH  A  6-iNCH  PHOTO- 
GRAPHIC TELESCOPE. 

TABLE  I. 


Exposure  Time. 

Measured 
d' 

Computed 

Constant 

C  —  Co 

1s 

0.0250 

0.0079 

0.0171 

2 

.0305 

.0136 

.0169 

4 

.0360 

.0192 

.0168 

8 

.0415 

.0248 

.0167 

16 

.0470 

.0305 

.0165 

32 

.0525 

.0361 

.0164 

64 

.0590 

.0417 

.0173 

128 

.0645 

.0474 

.0171 

256 

.0700 

.0530 

.0170 

On  the  hypothesis  that  the  standard  and  comparison  tele- 
scopes have,  photographically,  the  same  peculiarities,  the  theo- 
retical value  of  the  constant  term  for  the  33-inch  telescope  is 
given  by  the  expression 

«+  ft  log  Q'o  =  0.0055  +  0.0033  X  0.74  =  0.0079     (28) 

Polaris  being  taken  as  the  standard  star.  But  according  to 
observation  the  mean  constant  is  0.0248;  the  difference  between 
this  value  and  that  deduced  from  equation  (2)  must  be 
attributed  to  the  peculiarities  of  the  33-inch  lens  as  compared 
with  the  6-inch  standard  telescope.  The  explanation  of  this 
difference  seems  to  be  that  the  initial  images  do  not  start  from 
a  point,  but  from  a  sensible  area;  the  magnitude  of  this  area 
is  not  only  dependent  upon  the  diameter  of  the  objective  but 
also  upon  the  character  of  the  color  curve. 

The  photographic  magnitude  of  any  star  can  best  be  deter- 
mined by  making  two  or  more  exposures  on  the  same  plate,  so 


10  Terrestrial  Atmospheric  Absorption  of 

as  to  give  suitable  values  of  d'  for  determining  the  rate  of  growth 
of  the  image. 

The  law  expressed  by  equation  (2)  will  then,  it  seems,  hold 
good;  equations  (16)  and  (24)  being  used  to  find  the  proper 
magnitude. 

In  order  to  apply  the  formulae  to  any  particular  case,  the 
equivalent  value  of  d  should  not  be  much  less  than  0.0055,  as 
the  formulae  could  not  well  be  tested,  on  the  standard  star,  for 
values  of  t  less  than  one  second  of  time. 

The  number  of  examples  could,  of  course,  be  multiplied,  but 
for  the  present  purpose  the  foregoing  illustrations  are  deemed 
sufficient,  so  far  as  the  investigation  of  the  atmospheric  absorp- 
tion of  the  photographic  rays  of  light  is  concerned.  Later  on, 
in  dealing  with  the  data  given  by  the  WILLARD  lens,  this  sub- 
ject will  be  further  illustrated. 

The  foregoing  investigations  were,  of  course,  necessary  before 
the  observations  on  absorption  could  be  reduced.  To  enable 
any  one  to  follow  the  various  steps,  and  also  to  make  use  of  the 
tabular  values  for  other  purposes,  all  the  necessary  data  are 
given  in  abbreviated  form.  In  making  the  exposures  the 
observer  was  not  always  able  to  guard  against  those  causes 
which  produce  imperfect  images,  nor  was  it  always  possible  to 
know  before  the  developments  of  the  plates  whether  such  imper- 
fect images  were  present.  In  nearly  every  case  such  imperfec- 
tions are  in  the  nature  of  an  elongated  image,  caused  by  a  failure 
of  the  telescope  to  conform  to  the  diurnal  motion.  A  series  of 

dashes  ( )  indicate  that  the  particular  measure  was 

rejected  on  this  account. 

TABULAR  VALUES  OF  Q,  ra',  d,  AND  t. 

In  practice,  if  a  large  number  of  values  of  an  involved  ex- 
pression are  required,  the  ease  and  rapidity  with  which  such 
values  can  be  obtained  will  be  increased,  if  the  functions  corre- 
sponding to  certain  arguments  are  first  computed  and  then 
arranged  in  suitable  tabular  'form. 

I  have  accordingly  computed  the  values  d  for  certain  values 
of  t  and  equicrescent  values  of  Q.  These  quantities  are  arranged 
in  tabular  form.  (See  Table  II.) 

The  arguments  for  entering  this  table  are  the  measured  d 
and  the  corresponding  exposure  time  t.  The  corresponding 


The  Photographic  Rays  of  Light.  11 

provisional  magnitude  m'  is  there  found,  by  interpolation,  in 
the  first  horizontal  column  of  the  table. 

The  resulting  tabular  magnitudes  are  those  given  by  the  par- 
ticular DALLMEYEB  telescope  and  SEED  plates  No.  26,  used  in 
these  investigations.  For  convenience  and  completeness,  I  have 
retained  and  used  the  quantity  Q  throughout  the  whole  discus- 
sion in  preference  to  m',  as  the  value  of  Q  will  not  be  affected 
by  any  subsequent  change  in  the  light  ratio  which  it  may  be 
found  advisable  to  make  at  any  future  time.  I  have  therefore 
also  added  another  horizontal  argument  giving  the  values  of  Q. 

In  using  the  table  it  should  be  remembered  that  the  pro- 
visional unit  of  brightness  is  that  given  by  Polaris  at  the 
zenith-distance,  52°  40',  and  the  provisional  magnitude  at  that 
zenith-distance  is  2.00.  These  units  were  adopted  simply  as  a 
matter  of  convenience,  since  the  photographic  absorption  was 
not  known  until  the  present  investigation  was  completed. 

In  order,  however,  to  make  the  photographic  and  visual 
results  directly  comparable,  Polaris  will,  as  heretofore,  be  taken 
as  the  standard  star,  but  the  brightness  (1.00)  and  the  magni- 
tude (2.00)  finally  assigned  will  be  that  which  the  star  would 
have  if  it  could  be  observed  in  the  zenith  of  the  LICK  Obser- 
vatory. 

For  facilitating  the  use  of  Table  II  in  the  finally  adopted 
system  of  brightness  and  magnitude,  I  have  placed  the  new 
arguments,  corresponding  to  the  tabular  d,  at  the  bottom  of  the 
page. 

As  will  be  shown  farther  on,  the  atmospheric  absorption  of 
the  photographic  rays  at  52°  40'  zenith-distance  amounts  to  0.51 
magnitudes  on  the  provisional  scale,  consequently,  the  magni- 
tude of  Polaris  in  the  zenith  is  lm.49. 

If,  therefore,  we  adopt  2.00  as  the  photographic  magnitude  of 
Polaris  in  the  zenith,  we  have  simply  to  add  Om.51  to  each  of 
the  corresponding  tabular  arguments  for  magnitude  to  obtain 
the  new  tabular  arguments  for  magnitude. 

To  find  the  relation  which  exists  between  the  provisional 
tabular  values  of  Q,  and  the  corresponding  values  of  Q'  in  the 
new  system,  we  can  write  the  two  equations: 

Q2  =  (0.4)™-2  (29) 

2+wa  (30) 


12  Terrestrial  Atmospheric  Absorption  of 

Passing  to  logarithms,  and  taking  the  difference  between 
equations  (29)  and  (30),  we  readily  deduce  the  relation 

Q'  =  0.79  Q  (31) 

Hence,  having  given  the  tabular  value  of  Q  corresponding  to 
a  given  d  in  the  provisional  sj^stem,  we  have  only  to  multiply 
it  by  0.79  to  obtain  the  tabular  Q',  corresponding  to  the  same 
value  of  d  in  the  new  system. 

In  the  following  table  I  have  carried  the  tabular  quantities 
to  extreme  values  of  Q,  cZ,  and  f,  not  with  the  expectation  that 
the  relations  will  be  found  to  be  strictly  accurate  at  these  ex- 
treme limits,  but  rather  for  the  purpose  of  giving  a  general 
numerical  view,  so  to  speak,  of  the  whole  theory,  and  also  to 
more  easily  enable  others  to  compare  their  results  with  those 
here  given: 


The  Photographic  Rays  of  Light. 


18 


g       8 

d 


,s     fj^o     Ji 
So     ooo 


Opq 


ill 


5      q  q  q      q  q  q 


888 


38      &^. 


!2S    °i?ic 


•^888    8.88    888 

o 


*§!!  111  in  ||| 


J  OO        ^  —I  • 


(M  C^  CO        CO  CO  •<*< 

888    888 


I 


14 


J^errestrial  Atmospheric  Absorption  of 


r-lOCO          <MOOO 


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Is 


ll  1! 


O O 


1C  l^        O5  iH  ( 
COCD        CiCO< 


The  Photographic  Rays  of  Light.  15 

ATMOSPHERIC  ABSORPTION  OF  THE  PHOTOGRAPHIC  RAYS  OP  LIGHT. 

Owing  to  the  ever  changing  condition  of  our  atmosphere, 
and  to  the  want  of  definite  information  as  to  its  density  at 
different  heights  for  variations  in  temperature  and  pressure, 
the  complete  solution  of  the  problem  of  determining  the  path 
of  a  ray  of  star-light  has  not  yet  been  accomplished. 

Many  different  expressions  have  been  deduced  by  as  many 
different  investigators  for  the  law  of  atmospheric  refraction, 
and  in  all  of  these,  quantities  of  a  more  or  less  empirical  char- 
acter have  been  so  introduced  that  the  assumed  law  satisfied 
the  observed  data. 

The  determination  of  the  amount  of  star-light  lost  to  us 
during  its  transmission  through  our  atmosphere  seems  to  be  a 
still  more  complicated  problem.  In  the  case  of  refraction, 
observation  seems  to  show  that  the  relative  humidity,  for  in- 
stance, can  be  almost  wholly  neglected  so  far  as  its  effect  upon 
the  refraction  is  concerned.  The  same  may  be  said  of  other 
causes  which  do  not  affect  refraction  but  which  do  tend  to 
diminish  the  final  amount  of  light  which  would  otherwise  be 
received. 

It  is  probable  that  a  ray  of  light  in  passing  through  a 
medium  of  varying  density  suffers  not  only  internal  refraction, 
but  also  internal  reflection.  The  exact  amount  of  light  lost 
by  this  latter  property  has,  so  far  as  I  am  aware,  never  been 
determined. 

When,  in  addition  to  these  difficulties,  the  subject  is  further 
complicated  by  the  introduction  of  that  still  mysterious  agent, 
the  photographic  plate,  as  a  recorder  of  certain  data,  the 
task  of  satisfactorily  discussing  such  material  from  a  purely 
theoretical  standpoint  is  a  hopeless  one  at  the  present  state  of 
our  knowledge. 

A  consideration  of  these  difficulties  impelled  me  to  resort  to 
the  same  method  of  deducing  an  empirical  expression  which 
should  represent  the  terrestrial  atmospheric  absorption  of  the 
photographic  rays  of  light  that  I  had  used  in  deriving  the 
preceding  formula  for  finding  the  photographic  magnitudes  of 
the  fixed  stars. 

The  expressions  deduced  by  LA  PLACE,  SEIDEL,  MULLER, 
PICKERING,  and  others,  for  the  atmospheric  absorption  of  the 
visual  rays,  are  all  of  a  more  or  less  empirical  character. 


16  Terrestrial  Atmospheric  Absorption  of 

This  investigation,  like  the  preceding,  was  undertaken  at 
the  suggestion  of  Professor  HOLDEN.  Four  different  series  of 
observations  were  made,  as  follows: 


Second  Series. .At  Cayenne,  S.  A.,  in  Dec.,  1889 V.  S.  N.  O.  Telescope. 

Third  Series... At  Mt.  Hamilton,  in  July  and  Aug.,  1890.U.  S.  X.  O.  Telescope. 
Fourth  Series..  At  Mt.  Hamilton,  in  Nov.,  1891 Crocker  Telescope. 

The  exposures  for  the  third  series  were  kindly  made  for  me 
by  Professor  CAMPBELL,  who,  at  the  time,  was  spending  his 
vacation  at  the  LICK  Observatory.  The  exposures  of  the 
remaining  series  were  made  by  myself. 

METHOD  OF  OBSERVING. 

As  the  problem  under  consideration  is  one  which  can  be  said 
to  be  of  a  differential  character,  the  observations  and  reductions 
can  be  so  arranged  that  only  systematic  errors,  if  any,  need  be 
involved.  Such  errors,  so  far  as  the  effect  upon  the  final  result 
is  concerned,  can  be  practically  eliminated  in  the  reductions. 

To  accomplish  this  object,  certain  conditions  must  be  ful- 
filled. Among  others,  care  must  be  taken  that  during  the  time 
required  to  make  a  single,  complete,  and  independent  determi- 
nation, there  shall  be  no  changes  in — 

(1)  The  source  of  light. 

(2)  The  sensitiveness  of  the  photographic  films. 

(3)  The  atmospheric  conditions. 

(4)  The  focal  length  of  the  telescope,  as  defined  by  the  dis- 

tance from  the  objective  to  the  sensitive  film. 

(5)  The  development  of  the  plates. 

(6)  The  illumination  of  the  plates  while   they  are  being 

measured. 

All  the  above-mentioned  conditions  can  be  practically  ful- 
filled, as  will  appear  farther  on: 

First — To  secure  constancy  in  the  original  source  of  light. 
A  bright  star  should  be  selected  having  a  declination  some- 
where in  the  neighborhood  of  the  latitude  of  the  point  of 
observation,  and  whose  position  with  reference  to  the  observer's 
zenith  is  such  that  during  the  interval  between  the  time  of  the 
star's  meridian  passage  and  the  time  of  its  rising  or  setting,  the 
exposures  on  this  star,  at  various  zenith-distances,  are  free 
from  twilight  and  moonlight.  No  star  of  variable  light  should 
be  employed. 


The  Photographic  Rays  of  Light.  17 

Second — As  no  two  sensitive  plates,  taken  at  random  from 
the  same  box,  can  a  priori  be  said  to  be  of  positively  the  same 
degree  of  sensitiveness,  it  is  evident  that  the  only  way  to  secure 
uniformity  in  this  respect  is  to  make  all  the  exposures  for  a 
given  determination  on  the  same  plate;  and  even  here  we 
assume  that  the  film  is  equally  sensitive  in  all  its  parts,  which 
is  not  strictly  true. 

Third — Observations  made  under  abnormal  atmospheric 
conditions  (clear  at  one  altitude,  and  foggy,  smoky,  or  cloudy 
at  other  altitudes)  should  be  rejected. 

Fourth — In  order  to  be  sure  of  the  invariability  of  the  posi- 
tion of  the  sensitive  plate,  so  far  as  its  distance  from  the 
objective  is  concerned,  the  same  plate-holder  should  be  used 
for  all  the  exposures  of  a  single  determination;  and  all  the 
images  should  be  near  the  center  of  the  field. 

Both  the  second  and  fourth  conditions  are  fulfilled,  if  the 
same  plate  and  plate-holder  are  used. 

Fifth — As  all  the  images  of  any  given  series  will  now  be 
found  on  a  single  plate,  the  method  of  development  will  evi- 
dently be  the  same  for  all.  Different  plates  should  all  be 
developed  in  precisely  the  same  way. 

Sixth — It  is  very  essential  that  all  the  measures  of  a  given 
series  be  made  under  the  same  illumination;  too  much  stress 
cannot  be  laid  upon  this  condition.  As  all  the  exposures  will 
be  found  upon  a  single  plate,  this  condition  can  be  fulfilled  by 
making  all  the  measures  of  this  plate  at  a  single  sitting.  To 
avoid  the  effect  of  personal  equation,  all  the  measures  of  the 
present  paper  have  been  made  by  myself. 

METHOD  OP  DERIVATION  OF  THE  FUNDAMENTAL  EQUATION. 

To  determine  the  form  of  the  function  which  best  represents 
the  law  of  apparent  decrease  in  brightness  of  a  star  with  increas- 
ing zenith-distance,  the  theoretical  value  of  Q,  corresponding  to 
each  measured  d  for  exposures  of  2s,  4s,  and  8",  was  first  obtained 
with  the  aid  of  Table  II,  and  the  mean  of  the  separate  results 
adopted  as  the  value  of  Q  at  the  zenith-distance  corresponding 
~to  the  mean  of  the  times  of  observation. 

Empirical  equations  of  conditions  were  then  formed,  each 
value  of  Q  furnishing  the  constant  or  absolute  term  of  an  inde- 
pendent equation.  The  form  of  the  function  must  evidently  be 

9 


18  Terrestrial  Atmospheric  Absorption  of 

such  that  its  value  is  at  a  maximum  for  the  zenith-distance 
zero,  and  at  a  minimum  when  the  zenith-distance  is  at  a  maxi- 
mum. 

Several  of  the  simpler  formulae  which  I  deduced  repre- 
sented the  observed  data  quite  satisfactorily  for  zenith-distance? 
down  to  70°  or  75° ;  but  for  great  zenith-distances  all  these  first 
attempts  were  found  to  lack  generality,  the  residuals  near  the 
horizon  being  relatively  large,  and  of  a  systematic  character. 
After  several  tedious  trials  of  more  complicated  formula?,  in 
each  of  which  nearly  the  whole  mass  of  available  observations 
was  worked  over,  and  the  residuals  (obtained  by  subtracting 
the  empirical  values  from  the  observed)  discussed  by  a  com- 
bination of  graphical  and  analytical  results,  I  interpolated  the 
formula  given  below,  which  now  represents  the  observed  data, 
in  such  a  way  that  the  sum  of  the  squares  of  the  residuals  is 
less  than  it  is  for  any  of  the  other  formulae  discussed. 

If  B0  and  B  denote,  respectively,  the  photographic  magnitude 
of  a  star  at  the  zenith-distances  <2  =  o°  and  <?  =  <?",  and  if  / 
denotes  a  constant  depending  chiefly  upon  the  condition  of  the 
atmosphere,  the  equation  which  best  represents  the  observed 
data  is  of  the  form 

(32) 

In  this  expression  ^  is  to  be  regarded  as  an  abstract  number. 

the  square  of  which  represents  the  number  of  degrees  of  which 
the  trigonometrical  tangent  is  required. 

FIRST  SERIES  OF  OBSERVATIONS   FOR  ABSORPTION. 

All  the  observations  of  this  series  were  made  with  the  U.  S. 
N.  0.  telescope  already  referred  to.  This  instrument  was  set 
up  on  Mount  Hamilton,  so  as  to  have  a  clear  eastern  sky.  As 
there  was  no  covering  of  any  kind  to  protect  it  from  the  wind, 
which  is  often  quite  strong  here,  much  trouble  was  experienced 
from  this  source.  Besides  causing  a  vibration  of  the  whole 
instrument,  the  wind  very  frequently  stopped  the  driving  clock, 
which,  for  this  instrument,  is  governed  by  a  swinging  pendulum 
which  unlocks  the  train  of  wheelwork  at  every  half  vibration; 
sudden  variations  in  the  speed  being  checked  by  revolving  fans. 
This  form  of  governor  works  satisfactorily  so  long  as  the  resist- 


The  Photographic  Rays  of  Light.  19 

ance  to  be  overcome  by  the  clock  is  uniform.  If,  however,  for 
any  cause,  the  train  of  wheelwork  lags  so  that  the  pendulum 
reaches  the  unlocking  point  after  the  escapement  shaft  is  in 
proper  position,  the  clock  at  once  comes  to  a  standstill.  Later 
on  the  fans  were  inclosed  in  a  box,  which  improved  matters 
somewhat.  So  far  as  my  own  experience  goes  the  very  simple 
and  wholly  satisfactory  contrivance  now  so  largely  used  by 
American  instrument  makers  to  regulate  the  velocity  of  the 
centrifugal  or  rotary  pendulum  governor  is  much  to  be  pre- 
ferred. 

The  first  series  of  observations  for  atmospheric  absorption 
of  the  photographic  rays  was  made  on  a  Arietis.  I  should 
have  preferred  to  use  a  much  brighter  star,  but  this  one  seemed 
to  be  in  the  best  position  for  observation  at  both  great  and 
small  zenith-distances,  as  in  other  directions  the  view  was 
much  more  limited,  owing  to  the  proximity  of  the  Observatory 
buildings.  I  also  regret  that  in  the  original  program  it  was 
thought  to  be  sufficient  to  carry  the  observations  to  a  zenith- 
distance  of  only  75°.  (Later  on  I  secured  several  series  of 
observations  on  a  Lyrae  to  a  zenith-distance  of  90°.) 

At  each  altitude  exposures  of  2s,  4s,  and  8s  were  made  on  the 
same  plate,  the  telescope  being  slightly  shifted  after  each  expos- 
ure to  avoid  the  overlapping  of  the  different  images.  A  finding 
view  telescope  attached  to  the  tube  of  the  photographic  tele- 
scope was  furnished  with  a  suitable  network  of  wires,  so  that 
the  exposures  for  the  different  sets  could  be  properly  located. 

The  interval  of  time  between  the  exposures  at  different  alti- 
tudes was,  on  an  average,  less  than  one  hour. 

All  the  exposures  were  made  by  removing  the  cap  covering 
the  object-glass  as  quickly  as  possible  at  a  given  beat  of  the 
chronometer,  and  replacing  it  as  quickly  as  possible  at  another 
given  beat.  A  little  practice  enables  one  to  make  the  exposure 
times  of  the  proper  duration  with  a  very  small  percentage  of 
error  for  all  exposures  of  not  less  than  1s.  I  have,  however, 
deemed  it  best  to  use  only  the  exposures  which  are  greater 
than  1s. 

In  the  following  pages  the  comparison  between  theory,  as 
represented  by  equation  (32),  and  observation,  is  given  with 
sufficient  detail.  In  each  equation  of  condition  the  unknown 


20  Terrestrial  Atmospheric  Absorption  of 

quantities  involved  are  Q  (=  i/js )  and  /,  each  equation  being 
of  the  form 

«  — /??(3)  =  Q.  (33) 

which  «=  Q0;  £  =/,  or  /?  =  /  Q0;  and  ?  (5)  =  tan  [(0"']. 

Explanation  of  the  Tabular  Data  in   Tables  III- VII. 

The  first  column  gives  the  sidereal  time  corresponding  to  the 
mean  of  the  times  of  exposure.  The  corresponding  hour-angle 
(T),  zenith-distance  (£),  measured  diameters  (d),  and  result- 
ing values  of  Q  are  given  in  the  succeeding  columns  under 
those  headings.  The  last  column  gives  the  residual,  found  by 
subtracting  the  computed  theoretical  value  at  a  given  zenith- 
distance,  as  given  by  equation  (32),  from  the  observed  value  at 
the  same  zenith-distance. 

The  values  of  d  and  Q  for  the  separate  exposures  of  2s,  4s,  and 
8s  are  given  individually,  in  order  that,  first,  all  the  observed 
data  may  be  available  for  any  future  use,  and  second,  to  show 
more  plainly  how  closely  the  degree  of  accuracy  is  dependent 
upon  the  measured  d  corresponding  to  a  given  exposure  time  t. 
The  values  of  d  are  given  in  units  of  the  fourth  decimal  place 
of  inches. 

As  a  test  for  determining  the  sensitiveness  of  the  particular 
plate,  a  series  of  exposures  on  Polaris  were  also  made;  the 
results  will  be  found  in  Table  VIII,  which  also  gives  the 
provisional  relative  values  of  Q  and  m  for  both  Polaris  and 
of  Arietis.  The  last  column  gives  the  individual  results  of  the 
difference  between  the  magnitudes  of  these  two  stars.  The 
abnormal  condition  of  the  results  for  September  6th  is  shown 
to  be  the  same  for  both  stars. 

*  These  values  of  a  and  ft  have  no  relation  to  those  given  in  the  preceding 
pages. 


The  Photographic  Rays  of  Light. 


21 


U.  S.  N.  O.  Telescope.                       a  Arietis.                                Bar->  25in.87. 

Att,  Ther.,  76°. 

L.  O.,  Sept.  4,  1889.                            TABLE  III.                               Ex  ^  73<> 

d 

T 

T 

c 

2* 
43 

8' 

Q 

Mean 
Q 

o—  c 

42 

0.30 

»i»i8« 

18h  17m 

73°.l 

54 

0.50 

0.45 

+  0.05 

63 

0.55 

20   55 

18    54 

66  .0 

52 
62 

0.45 
0.55 

0.50 

+  0.02 

50 

0.50 

21    33 

19   32 

58  .4 

59 

0.60 

0.57 

+  0.02 

66 

0.60 

48 

0.45 

22    48 

20   47 

43.5 

59 

0.60 

0.57 

—  0.07 

68 

0.65 

56 

0.70 

0     0 

21   59 

29  .7 

63 

0.70 

0.70 

+  0.01 

55 

0.65 

0    10 

22     9 

27  .8 

65 

0.70 

0.72 

+  0.02 

75 

0.80 

56 

0.70 

1     3 

23     2 

18  .9 

63 

0.70 

0.70 

—  0.02 

72 

0.70 

Equations  of  Condition. 

a  —  0.76  /?  =  0.45 
a  —  0.58/5  =  0.50 
a  —  0.44/3=0.57 
a  —  0.23  /?  =  0.57 
or  — 0.11  /3  =  0.70 
a  —  0.09  /?  =  0.72 
«  —  0.04  /?  =  0.70 

Normal  Equations. 

7.00  a  —  2.25  /3  =  4.21 
2.25  a—  1.18 /?=  1.15 

Solution  of  Normals. 

<x  =  0.743 
y3  =  0.443 


(34) 


(35) 


(36) 


22  Terrestrial  Atmospheric  Absorption  of 


U.  S.  X.  0.  Telescope.                     a  Arietis.                                 Bar-.  %>"•& 

Att.,  71°. 

L.  O.,  Sept.  5,  1889.                             TABLE  IV.                                    Ex-)  710> 

d 

T 

r 

C 

2s 

4s 

Q            ^ 

o—c 

8' 

40 

0.30 

19»  45m 

jyh  4401 

79°.4 

45 

0.30 

0.33 

-0.12 

55 

0.40 

55 

0.65 

21      1 

19     0 

64  .8 

60 

0.60 

0.65 

—  0.06 

70 

0.70 

60 

0.80 

21    47 

19   46 

55.0 

67 

0.80 

0.87 

+  0.05 

85 

1.00 

65 

1.00 

23   28 

21    27 

35.1 

77 

1.05 

1.03 

+  0.06 

87 

1.05 

67 

1.05 

0   43 

22    42 

22  .3 

77 
90 

1.05 
1.10 

1.07 

+  0.05 

Equations  of  Condition. 

^  —  0.96  ,5  =  0.33 
a  —  0.56,5  =  0.65 
a  —  0.38,5  =  0.87 
a  — 0.15,5=1.03 
a-  0.06,5=1.07 

Normal   Equations. 
5.00  a—  2.11  ,5  =  3.95 
2.11  or  — 1.59  ,5=1.22 

Solution  of  Normals. 
a=  1.057 
P  =  0.633 


(37) 


(38) 


(39) 


T/te  Photographic  Rays  of  Light. 


23 


r.  s.  X.  O.  Telescope. 
L.  0.,  Sept,  6,  1889. 


a  Arietis. 
TABLE  V. 


Bar.,  25">.90. 
Att.,  71°. 
Ex.,  71°. 


T 

T 

I 

2s 
4* 
8' 

Q 

Mean 
Q 

o—  c 

30 

0.15 

IQh  40m                    lyh  39m 

80°.3 

40 

0.25  !           0.23 

+0.04 

45 

0.30 

35 

0.20 

21     3 

19     2 

64.6 

45 

0.30 

0.28 

—  0.03 

50 

0.35 

40 

0.30 

21    53                19   52 

54  .4 

45 

0.30 

0.33 

-0.02 

55 

0.40 

40 

0.30 

23     4                21     3 

40  .3               50 

0.40 

0.37 

—  0.03 

55 

040 

45 

0.40 

00           !     21    59 

29.7 

55 

0.50 

0.47 

+  0.05 

1 

60 

0.50 

Equations  of  Condition. 

a  —  0.99,5  =  0.23 
a  —  0.55  ,3  =  0.28 
a  —  0.37/5  =  0.33 
a  —  0.20,5  =  0.37 
or  — 0.11  ,5  =  0.47 

Normal  Equations. 
5.00  a—  2.22/5=  1.68 
2.22  a  — 1.47/5=0.62 

Solution  of  Normals. 

a  =  0.452 
,*  =  0.261 


(40) 


(41) 


(42) 


24  Terrestrial  Atmospheric  Absorption  of 


U.  S.  N.  0.  Telescope. 
L.  O.,  Sept.  7,  1889. 


a  Arietis. 
TABLE  VI. 


Bar.,  25«».87. 
Att.,  72°. 
Ex.,  72°. 


r 

r 

c 

d 

Q 

Mean 
Q 

0—  C 

20"  21" 

18"  20" 

72°  .6 

50 
60 

0.50 
0.60 

0.55 

0.00 

21  29 

19  28 

59.2 

60 
70 
70 

0.80 

0.85 
0.70 

0.78 

+  0.01 

22  17 

20  16 

49.7 

60 
70 
85 

0.80 
0.85 
1.00 

0.88 

0.00 

23  15 

21  14 

38  .1 

65 
75 

85 

1.00 
1.00 
1.00 

1.00 

+  0.04 

0  31 

22  30 

24.2 

65 
75 
90 

1.00 
1.00 
1.10 

1.03 

—  0.03 

Equations  of  Condition. 

a  —  0.74,3  =  0.55 
a  —  0.45  ,5  =  0.78 
a—  0.31  ,3  =  0.88 
a  —  0.18,5  =  1.00 
a  — 0.07,3  =  1.03 

Normal  Equations. 

5.00  a  — 1.75,5  =  4.24 
1.75  a  — 0.88,3  =  1.28 

Solution  of  Normals. 

a =1.113 

,3  =  0.758 


(43) 


(44) 


(45) 


The  Photographic  Rays  of  Light. 


25 


V.  S.  X.  O.  Telescope. 
L.  0.,  Sept.  14,  1889. 


a  Arietis. 
TABLE  VII. 


Bar.,  25i°.83. 
Att.,  67°. 
Ex.,  67°. 


T 

* 

r 

d 

2' 
4* 

8s 

Q 

Mean 
Q 

0  —  C 

49      0.50 

20"  18-" 

18"  17m     73°.l 

53     0.45 

0.50 

+  0.02 

62     0.55 

51     0.55 

20  55 

18  54 

66  .0 

57     0.55 

0.58 

+  0.02 

67 

0.65 

52 

0.55 

21  33 

19  32 

58  .4 

62 

0.65 

0.63 

—  0.01 

1 

72 

0.70 

55 

0.65 

22  48 

20  47     43  .5 

65  I    0.70 

0.72 

—  0.02 

75  !     0.80 

57  i     0.70 

0  3 

22  2     29  .1 

67     0.80 

0.80 

—  0.01 

80 

0.90 

60 

0.80 

0  10 

22  9 

27  .9 

67 

0.80 

0.83 

+  0.02 

80 

0.90 

60 

0.80 

1  0 

22  59     19  .3 

67     0.80 

0.83 

—  0.01 

80     0.90 

Equations  of  Condition. 

a  —  0.75,5  =  0.50 
a  —  0.58  ,3  =  0.58 
a  —  0.44,5  =  0.63 
a  —  0.23,5-0.72 
a  —  0.10/5  =  0.80 
a  —  0.09  ,5  =  0.83 
a—  0.04/5  =  0.83 

Normal   Equations. 
7.00^  —  2.23,5  =  4.89 
2.23  a—  1.14,5=1.34 

Solution  of  Normals. 
a  =  0.862 
=  0.510 


(46) 


(47) 


(48) 


NOTE. — In  the  following  table  it  should  be  remembered  that  for  Polaris  the 
Q0  refers  to  a  zenith-distance  52°  40*,  while  for  a  Arietis,  it  corresponds  to  the 
zenith-distance  0°.  The  same  remark  is  to  be  applied  to  the  comparisons 
with  other  stars. 


26  Terrestrial  Atmospheric  Absorption  of 


TABLE  VIII. 


Polaris. 

<?» 

m' 

A  m' 

Date. 

d 

c 

Polaris. 

a 
Arietis. 

Polaris. 

a 

Ariel  in. 

1889. 
Sept.  4 

60 
65 
75 

65 
75 

85 

55 
60 
65 

65 
75 
90 

60 

75 
90 

0.80 
0.85 
0.90 

1.00 
1.00 
1.00 

0.50 
0.60 
0.60 

1.00 
1.00 
1.10 

0.53 
0.66 
1.10 

0.85 
1.00 
0.57 
1.03 
076 

0.74 
1.06 
0.45 
1.11 

0.86 

2.54 
2.00 
3.L2 
1.93 
2.59 

2.65 
1.88 
3.74 
1.78 
2.33 

—  0.11 
+  0.12 
—  0.52 
+  0.15 
+  0.26 

Sept.  5  
Sept.  6  

Sept.  7 

Sept.  14 

The  mean  zenith-distance  of  a  Arietis,  the  atmospheric  press- 
ure and  temperature,  and  the  resulting  values  of  /,  are  given 
in  Table  IX. 

a  Arietis. 
TABLE  IX. 


Date. 

Mean 
Zenith- 
Distance. 

Pressure. 

Temper- 
ature. 

/=! 

HEM  ARKS. 

1889. 
Sept.  4. 

45°.3 

25in.76 

73° 

0.60 

Sept  5 

51  3 

25    79 

71 

060 

Sept.  6 

53  .9 

25  .80 

71 

058 

Moon. 

Sept.  7 

48  .8 

25  .77 

72 

0.68 

Moon  and  smoke. 

Sept.  14  

45  .3 

25  .74 

67 

0.59 

The  Photographic  Rays  of  Light.  27 

That  the  plates  exposed  on  a  Arietis  were  not  all  of  the  same 
degree  of  sensitiveness  seems  to  be  quite  plainly  shown  by  the 
results  given  in  Table  VIII,  where  the  magnitude  of  Polaris, 
as  deduced  from  its  uncorrected  measured  images,  varies  all 
the  way  from  lm.93  on  September  7th  to  3m.22  on  September 
6th.  That  this  variation  is  not  due  to  errors  of  observation 
follows  from  the  fact  that  the  range  in  magnitude  of  a  Arietis, 
using  the  uncorrected  measures,  is  also  greatest  for  these  same 
dates. 

The  plate  exposed  September  6th  was  the  least  sensitive,  and 
that  exposed  September  7th  the  most  sensitive  of  the  whole  set. 

A  part  of  this  difference  in  magnitude  for  different  dates 
may  of  course  be  due  to  different  atmospheric  conditions,  the 
air  being  more  free  from  foreign  matter  at  one  time  than 
another. 

So  far  as  the  meteorological  conditions  of  pressure  and  tem- 
perature are  concerned,  the  range,  as  shown  in  Table  IX,  is 
entirely  too  small  to  account  for  any  considerable  portion  of 
variation  in  the  computed  results;  for  this  same  reason  no 
reliable  inferences  can  be  drawn  from  this  series  as  to  the  effect 
of  pressure  and  temperature  on  the  absorption  of  the  photo- 
graphic rays. 

A  difference  in  the  development  of  the  plates  would  also 
cause  a  variation  of  precisely  this  kind,  and  this  particular 
phase  of  the  investigation  will  be  treated  more  fully  farther 
on.  In  this  place  I  only  wish  to  call  attention  to  the  fact  that 
those  plates  which  give  results  indicating  greater  sensitiveness 
(whether  such  is  the  actual  case  or  not)  give  as  a  rule  larger 
values  of  /  than  those  plates  which  appear  to  be  less  sensitive. 
Compare,  for  instance,  m  and  the  corresponding  value  of  /  for 
the  same  plate  in  the  above  tables. 

If  we  take  the  mean  of  all  the  results  for  a  Arietis,  giving 
the  observations  of  each  night  the  same  weight,  we  obtain  the 
following  expression  for  atmospheric  absorption  of  the  photo- 
graphic rays  expressed  in  brightness: 


=  £0l— 0.61  tp  (<?)  (49) 


28  Terrestrial  Atmospheric  Absorption  of 


DISCUSSION    OF    THE     SECOND    SERIES    OF    OBSERVATIONS    FOR 
ABSORPTION. 

The  second  series  of  observations  for  absorption  was  made  in 
Cayenne,  South  America,  to  which  place  the  LICK  Observa- 
tory was  enabled  to  send  an  eclipse  expedition  through  the 
liberality  of  Hon.  CHARLES  F.  CROCKER,  a  Regent  of  our  State 
University.  The  eclipse  observers  from  this  Observatory  were 
S.  \V.  BURNHAM  and  the  writer.  C.  H.  ROCKWELL,  of  Tarry- 
town,  New  York,  also  joined  our  party  as  a  volunteer  observer. 

In  addition  to  the  regular  work  of  the  eclipse  expedition  it 
was  my  intention  to  make  an  extended  series  of  observations 
on  a  large  number  of  bright  stars,  for  the  purpose  of  determin- 
ing their  photographic  magnitudes,  and  also  to  make  a  very 
complete  series  of  observations  on  atmospheric  absorption  of 
the  photographic  rays.  That  this  plan  of  work  was  not  as 
completely  carried  out  as  originally  intended  must  be  attributed 
wholly  to  the  extremely  unfavorable  condition  of  the  weather. 
During  our  entire  stay  of  one  month  clouds  were  never  wholly 
absent  from  the  sky  during  an  entire  night,  and  ordinarily  the 
difference  between  the  dry  and  wet  bulb  thermometers  was  only 
a  degree  or  two. 

I  believe  it  rained  on  nearly  every  day  of  our  stay  in  Cay- 
enne. Clouds  would  at  times  suddenly  form  in  the  clearest 
sky,  so  that  in  making  exposures  it  was  very  necessary  for  the 
observer  to  keep  the  closest  watch  for  perfectly  clear  spaces. 

Another,  and  even  greater,  source  of  annoyance  was  the  con- 
stant tendency  of  the  objective  to  become  covered  with  dew. 
If  reliable  results  were  to  be  obtained  it  was  evidently  useless 
to  make  exposures  with  a  lens  (only  incompletely  wiped  off 
with  a  dry  cloth)  which  might  fog  over  before  the  2s,  4s,  and  8s 
exposures  could  be  completed. 

After  my  first  night's  experience  I  kept  a  large  tin  can,  which 
was  open  at  one  end,  near  the  instrument.  This  can  was  kept 
in  a  heated  state  during  the  whole  time  the  observations  were 
going  on,  by  placing  it  in  an  inverted  position  over  a  burning 
lamp.  Just  before  making  the  exposures  this  can  was  placed 
over  the  objective  end  of  the  tube,  and  allowed  to  remain  there 
until  the  heated  air  within  the  can  dispelled  the  dew.  Often  it 
was  necessary  to  reheat  the  can  several  times  before  the  desired 
effect  could  be  produced. 


The  Photographic  Rays  of  Light.  29 


As  all  the  exposures  were  made  east  of  the  meridian  the 
early  observations  would  correspond  to  those  made  at  great 
zenith-distances.  The  instrument  at  these  times  would,  ordi- 
narily, be  still  somewhat  warm  from  the  day  temperature,  and, 
consequently,  the  objective  would  be  more  apt  to  be  wholly  free 
from  dew  than  would  be  the  case  later  in  the  evening  when  the 
stars  used  would  be  at  a  greater  altitude.  The  effect  of  dew  on 
the  objective  would,  for  a  moderately  faint  star,  of  course  tend 
to  diminish  the  size  of  the  images  on  the  photographic  plate, 
while  for  very  bright  stars,  like  ft  Orionis  and  Sirius,  there 
would  also  be  a  blurring  of  the  image  over  a  considerable  larger 
area  than  that  occupied  by  the  normal  image.  On  the  whole, 
therefore,  it  is  quite  probable  that  the  later  exposures,  in  spite 
of  the  precautions  taken,  gave  images  which  were  of  less  diam- 
eter than  would  have  been  obtained  earlier  in  the  evening  for 
an  equal  altitude. 

A  very  striking  case,  illustrating  this  phase  of  the  problem, 
is  shown  on  a  plate  exposed  on  December  13th.  From  Oh  37m 
to  2h  18™,  sidereal  time,  the  images  of  ft  Orionis  increased  accord- 
ing to  the  usual  experience,  but  after  2h  30m  the  images  of  this 
star  actually  began  to  decrease  in  size,  although  the  star  had 
not  yet  reached  the  meridian.  The  peculiar  appearance  of  the 
images  and  the  blurred  outline  of  the  trail,  shown  after  devel- 
opment, at  once  indicated  that  something  was  wrong.  On 
referring  to  my  note-book  the  words,  "  objective  covered  with 
deAV  at  close  of  observations,"  cleared  up  the  mystery.  After 
this  night's  work,  which  was  the  first  made  use  of  in  Cayenne, 
the  above  mentioned  precautions  were  taken  to  keep  the  object- 
ive as  free  from  dew  as  possible.  The  2s,  4s,  and  8s  exposures 
were  always  made  at  times  when  the  star  appeared  to  be  at  least 
several  degrees  from  the  nearest  clouds,  and,  so  far  as  the 
observer  could  judge,  of  normal  brightness.  It  was  often  neces- 
sary to  wait  half  an  hour  or  more  before  a  suitable  exposure 
could  be  made.  After  each  set  of  exposures  the  star  was  allowed 
to  trail  for  one  minute.  These  trails,  in  many  instances,  show 
the  effects  of  passing  clouds.  From  the  foregoing  statements  it 
is  evident  that  the  results  obtained  for  Cayenne  are  not  as  trust- 
worthy as  is  desirable. 

As  the  data  given  in  the  following  tables  are  arranged  in  the 
same  way  as  for  the  first  series,  no  separate  explanation  need  be 
given  here. 


Terrestrial  Atmospheric  Absorption  of 


U.  s.  X.  O.  Telescope. 
Cayenne,  Dec.  13, 1889. 


a  Orionis. 
TABLE  X. 


Aneroid,  30"' .0. 
Dry  Ex.,  76° .0. 
Wet,  75°  .5. 


T 

T 

c 

2s 

4- 

8* 

Q 

Mean 
Q 

o—  c 

50 

0.50 

Qh  28m 

18"  39™     79°.7 

60 

0.60 

0.60 

—  0.02 

70 

0.70 

60 

0.80 

0  51     !  19  2 

74  .0 

70 

0.85 

0.85 

+  0.07 

80 

0.90 

60 

0.85 

1  8 

19  19 

69  .8 

70 

0.85 

0.88 

0.00 

85 

1.00 

65 

1.00 

1  22 

19  33 

66  .3 

75 

1.00 

1.03 

+  0.08 

90 

1.10 

65 

1.00 

1  46 

19  57 

60.4 

75 

1.00 

1.00 

—  0.06 

S5 

1.00 

65 

1.00 

2  9* 

20  20 

54  .7 

80 

1.15 

1.08 

-0.06 

90 

1.10 

*  Object-glass  covered  with  dew;  images  from  here  on  begin  to  decrease 
in  diameter  (on  the  plate)  with  diminishing  zenith-distance. 

Equations  of  Condition. 

a  —  0.97  fi  =  0.60 
a  —  0.78/5=0.85 
a  —  0.67/5  =  0.88 
a  —  0.59/5=1.03 
a  —  0.47/5=1.00 
^—0.38^=1.08 


(50) 


Normal  Equations. 

6.00  a  —  3.86/5=5.44 
3.86  or  —  2.71  /?=3.30 

Solution  of  Normals. 


(51) 


=  0.8S 


(52) 


The  Photographic  Rays  of  Light. 


U.  S.  X.  0.  Telescope. 
Cayenne,  Dec.  13,  1889. 


Rigel. 
TABLE  XI. 


T 

r 

S 

d 
» 

4s 

8-' 

Q 

Mean 
Q 

o  —  c 

REMARKS. 

90         2.30 

That    the    object- 

0"  37"' 

19»  28"'        69°  .5 

110         2.20 

135  j       2.30 

2.27 

—  0.04 

glass     gradually 
became    covered 

095         2.60 

with  dew  is  plain- 
ly shown  on  the 

0   57 

19   48 

64  .2 

115         2.40 

2.47 

—  0.03 

glass      negative; 

140         2.40 

the  images  after 

2h     41m    are    all 

1    14 

20     5 

60  .1 

95 
125 
145 

2.60 
2.80 
2.60 

2.67 

+  0.08 

blurred  and  very 
indistinct;     they 
have,    therefore, 

been   wholly  re- 

90 

2.30 

jected. 

1    30 

20   21 

56  .2 

120 

2.60 

(2.43) 

140 

2.40 

100 

3.00 

1   52 

20   43          50  .9 

130 

3.00 

2.90 

—  0.05 

150 

2.70 

105 

2.30 

2    18 

21     9 

44  .6 

125 

2.80 

2.93 

—  0.05 

150 

2.70 

105 

3.30 

2    41 

21   32 

39  .2 

130 

3.00 

3.10 

+  0.05 

160 

3.00 

Equations  of  Condition. 

a  —  0.66/5  =  2.27 
a  —  0.54/5  =  2.47 
a  —  0.47  /?  =  2.67 
a  —  0.40/3  =(2.43) 
a  —  0.32  yS  =  2.90 
a  —  0.24 /?=  2.93 
a  —  0.19  p  =  3.10 

Normal  Equations. 

6.00  a  —  2.42  /?  =  16.34 
2.42  a  — 1.15/3=    6.31 

Solution  of  Normals. 
a  =  3.37 


(53) 


(54) 


(55) 


32  Terrestrial  Atmospheric  Absorption  of 


4 
r.  s.  N.O.  Telescope.                      a  Orionis.                            Aneroid,    29*92. 
Thor    »Drv,  80-.0. 
Cayenne,  Dec.  15,  1889.                  TABLE  XII.                              her'  •(Wet,76°.0. 

r 

T 

c 

d 
2» 
4s 

8» 

Q            M^fn 

0    56 
1   31 
2     4 
2   30 
3     3 
4     4 
5    14 
5    49 

18»40°> 
19     7 
19   42 
20    15 
20   41 
21    14 
22    15 
23   25 
0     0 

77°.2 
72  .8 
64  .1 
55  .9 
49  .5 
41  .3 
26  .2 
9  .0 
2  .3 

1 

0  70               006 

70 

60 
70 
80 

65 

0.70 

0.80 
0.85 
0.90 

1.00 

0.85          +0.01 
1.05          +0.09 
1.00          —  0.04 
1.15          —  0.05 
1.17          —0.01 
1.22          —  0.01 
1.22          —  0.05 

1.33          +0.05 

i 

90 

65 
75 

85 

70 

1.10 

1.00 
1.00 
1.00 

1.20 

90 

70 
80 
90 

70 

1.10 

1.20 
1.20 
1.10 

1.20 

95 

70 
80 
95 

75 
85 
95 

1.25 

1.20 
1.20 
1.25 

1.45 
1.30 
1.25 

Equations  of  Condition. 
«  —  0.88  /?  =  0.70 
oc  —  0.75  ft  =  0.85 
oc  —  0.54/2=1.05 
a  —  0.40/3=1.00 
«  — 0.31  /?=1.15 
<*  — 0.21  /?=1.17 
«  — 0.08 /?=  1.22 
«  —  0.01  /?=1.22 
a  —  0.00  ft=  1.33 

Normal  Equations. 
9.00  a  —  3.18/3  =  9.60 
3.18  «  — 1.93/3  =  2.95 

Solution  of  Normals. 
a=U28 

ft  =  0.59 


(56) 


(57) 
(58) 


The  Photographic  Rays  of  Light. 


U.  S.  X.  O.  Telescope. 
Cayenne,  Dec.  15, 1889. 


Procyon. 
TABLE  XIII. 


Aneroid,  29iQ.92. 

Tho.    'Dry,  80°. 
Ther.  '0 


T 

T 

c 

d 

& 

4s 

8s 

Q 

Mean 
Q 

o—  c 

!h54m 

18"  21m 

84°  .4 

47 

57 

0.35 
0.45 

0.40 

—  0.19 

2  12 

18  39 

79  .9 

65 

72 

1.00 
0.90 

0.95 

+  0.08 

2  52 

19  19 

69  .9 

90 
105 

1.50 
1.50 

1.50 

+  0.17 

3  27 

19  54 

61  .2 

82 
97 
110 

1.90 
1.70 
1.60 

1.73 

+  0.14 

4  10 

20  37 

50  .5 

85 
97 
115 

2.00 
1.75 
1.75 

1.83 

+  0.01 

5  40 

22  7 

28.1 

87 
102 
122 

2.15 
1.95 
1.90 

2.00 

—  0.16 

Equations  of  Condition. 

a  — 1.17/5  =  0.40 
a  —  0.98  /3  =  0.95 
a-  0.67  /3=  1.50 
a  —  0.49/3=1.73 
a  —  0.32  /3=1.83 
a  —  0.10/5=2.00 

Normal  Equations. 

6.000-  —  3.73  /?  =  8.41 
3.73 a—  3.13  /?  =  4.04 

Solution  of  Normals. 
a  =  2.31 
/?=1.47 


(59) 


(60) 


(61) 


34  Terrestrial  Atmospheric  Absorption  of 


U.  8.  N.  0.  Telescope. 
Cayenne,  Dec.  16, 1889. 


a  Orionis. 
TABLE  XIV. 


Aneroid,  29in.90. 


T 

r 

c 

d 

2* 
43 

8s 

Q 

Mean 
Q 

o  —  c 

60 

0.80 

Oh47m 

18"  58"" 

75°.0 

70 

0.85 

0.85 

—  0.02 

80 

0.90 

65 

1.00 

1  23 

19  34 

66  .1 

1.00 

—  0.01 

67 

1.10 

1  51 

20  2 

59  .2 

1.12 

_|_0.02 

90 

1.15 

70 

L20 

2  20 

20  31 

52  .0 

80 

1.15 

1.17 

—  0.01 

90 

1.15 

75 

1.45 

3  25 

21  36 

35  .9 

85 

1.30 

1.33 

+  0.04 

95 

1.25 

75 

1.45 

5  45 

23  56 

2  .8 

85 

1.30 

1.37 

—  0.03 

Equations  of  Condition. 

«  — 0.81  /5  =  0.85 
a  —  0.59  0=  1.00 
a  —  0.45  /3=  1.12 
a  —  0.34/5=1.17 
a  —  0.16/5=1.33 
a  — 0.00/5=1.37 

Normal  Equations. 
6.00  or  —  2.35/5=6.84 
2.35  «— 1.36)3=2.39 

Solution  of  Normals. 
a  =  1.40 


(62) 


(63) 


(64) 


The  Photographic  Rays  of  Light. 


35 


U.  S.  X.  O.  Telescope. 
Cayenne,  Dec.  16,  1889. 


Sirius. 
TABLE  XV 


T 

T 

c 

d 
2* 
4* 

8' 

Q 

Mean 
Q 

o  —  c 

lh  I7m 
1  57 

3  28 
4  59 

Igh  37m 

19  17 
2048 
22  19 

82°  .6 
73  .1 
52  .1 
32  .9 

87 
100 

100 
125 
140 

115 
140 
190 

120 

1.40 
1.35 

2.95 

2.80 
2.60 

4.00 
3.40 
3.90 

4.40 

1.37 

2.78 
3.77 
4.30 

—  0.14 
+  0.23 
—  0.06 
—  0.19 

5  51 

23  11 

24  .7 

200 

125 
175 

220 

4.20 

4.80 
4.90 
4.80 

4.83 

+  0.15 

Equations  of  Condition. 

a  — 1.08/5=1.37 
a  —  0.75  /3=  2.78 
a  —  0.34  ft  =  3.77 
a  —  0.13/3  =  4.30 
a  —  0.07  /3  =  4.83 

Normal  Equations. 

5.00  a  —  2.73/3=17.05 
2.73  or— 1.87/3=   5.74 

Solution  of  Normals. 
a  =  4.90 


(65) 


(66) 


(67) 


36  Terrestrial  Atmospheric  Absorption  of 


In  Table  XVI  are  given  the  mean  values  of  <2,  pressurer 
temperature,  Q0,  and /for  each  date  and  star. 


TABLE  XVI. 


Date. 

Star. 

Mean 
Z.-D. 

Pressure. 

Temper- 
ature. 

Qo 

/=! 

1889. 

December  13.  } 
December  15.  V 
December  16  J 

a  Orionis. 

(      67°.5 
{       44  .3 
[      48  .5 

SO'a.OO 
29   .92 
29   .90 

76° 
80 

1.47 
1.28 
1.40 

0.59 
0.46 
0.47 

December  13-.. 

Rigel. 

55  .0 

30   .00 

76 

3.37 

0.4& 

December  15.  .. 
December  16 

Procyon. 
Sinus. 

62  .3 
53  .1 

29  .92 
29  .90 

80 

2.31 
4.90 

0.64 
0.64 

The  separate  results  for  the  value  of  /=-£  as  found  for 
Cayenne  at  sea-level  are  given  in  Table  XVII. 


TABLE  XVII. 


Star. 

/-I 

Weight. 

a  Orionis  .. 

0.51 

1 

Rigel  
Procyon  
Sinus  

0.46 
0.64 
0.64 

1 
2 
4 

In  the  column  headed  "  weight,"  a  Orionis  has  been  given 
such  small  weight,  firstly,  because  it  is  a  variable  star,  and 
secondly,  because  its  spectral  type  is  different  from  the  other 
stars,  and  consequently  the  coefficient  of  absorption  may  be 
different.  To  Rigel  has  been  assigned  the  same  weight,  because 
it  was  only  used  on  the  first  night,  for  which  the  conditions 
were  rather  uncertain.  In  the  case  of  Procyon  the  zenith- 
distance  was  greater  than  for  any  of  the  other  stars,  while  for 
giving  good  measurable  images  of  a  star  near  the  horizon 
Sirius  is  by  far  the  best  source  of  stellar  light.  Polaris  was 
photographed  on  two  occasions;  the  data  and  results  are  given 
in  Table  XVIII. 


The  Photographic  Rays  of  Light. 


Cayenne,  Dec.,  1889. 


Polaris. 
TABLE  XVIII. 


d 

8s 

Q 

ra' 

32" 
64* 

Obs. 

Comp. 

Obs. 

Comp. 

50 

0.35 

Dec.  15.. 

2   30 

1    12 

83°.7 

1.14 

55 
60 

0.35 
0.40 

0.37 

0.40 

4.17 

3.99 

65 

0.40 

55 

0.40 

Dec.  17.. 

3   18 

2   0 

83.8 

1.14 

60 
65 

0.40 
0.45 

0.42 

0.40 

3.89 

3.99 

70 

0.45 

To  obtain  the  computed  values  of  Q,  it  must  be  remembered 
that  Polaris  has  been  given  the  brightness  1.00,  and  the  pho- 
tographic magnitude  2.00  for  a  zenith-distance  equal  to  the 
latitude  of  Mount  Hamilton. 

As  found  from  both  the  preceding  Mount  Hamilton  series 
and  the  Cayenne  observations,  the  value  of  the  factor/  is  very 
nearly  0.60.  In  the  equation 


Q=Q0(l- 0.60  <?(<?)) 


(68) 


We  must  place  Q  =  l  and  <2  =  52°  40',  and  solve  for  Q0. 
this  value  of  <§  we  have  <p  (<2)  =  0.35;  hence, 


For 


=  1.26 


(69) 


Substituting  this  value  of  Q0  in  equation  (70),  and  placing 
<p  (£)  =  1.14,  we  obtain  the  tabulated  value  0.40  for  Q;  the 
corresponding  magnitude  is  3.99.  The  mean  of  the  two 
observed  photographic  magnitudes  is  4.03;  the  practical  agree- 
ment between  theory  and  observation  is  therefore  all  that  could 
be  desired. 

Taking  the  weighted  mean  of  all  the  determinations  made 
at  Cayenne,  we  have  the  expression 


B  =  B0(i—  0.59  g> 


(70) 


One  would  naturally  expect  that  at  sea-level  the  value  of 
the  factor  /  should  come  out  greater  than  for  a  considerable 
altitude,  but  the  figures  do  not  show  such  a  condition  of  things. 


38  Terrestrial  Atmospheric  Absorption  of 


Perhaps,  however,  the  effect  of  dew  on  the  object-glass  has  not 
been  completely  eliminated.  If  a  simultaneous  series  of  obser- 
vations had  been  carried  on  for  decreasing  star-altitudes,  the 
effect  of  a  gradual  dewing  of  the  object-glass  would  have  been 
to  cause  an  increase  in  resulting  value  of  /. 

In  a  clear  sky  the  stars,  at  considerable  altitudes,  appeared 
fully  as  bright  at  Cayenne  as  they  do  on  Mount  Hamilton,  so 
far  as  the  observer  could  judge  by  estimation. 

DISCUSSION    OF     THE     THIRD     SERIES    OF     OBSERVATIONS    FOR 
ABSORPTION. 

After  our  return  from  Cayenne  the  U.  S.  N.  0.  telescope  was 
again  set  up  on  Mount  Hamilton,  and  a  third  series  of  observa- 
tions undertaken.  At  the  time  I  was  busily  engaged  on  "A 
Mechanical  Theory  of  the  Corona,"  so  Professor  CAMPBELL 
kindly  consented  to  make  the  exposures  of  this  series  for  me 
while  the  DALLMEYER  telescope  was  still  available. 

As  in  the  first  series,  there  chanced  to  be  no  suitable  very 
bright  star  on  which  the  exposures  could  be  made.  It  was 
finally  decided  to  use  ex  Andromedae. 

To  utilize  the  whole  time  available  for  making  suitable 
exposures,  five  different  plate-holders  were  used.  Each  plate- 
holder  was  carefully  fitted  to  the  tube,  so  that  the  sensitive 
film  in  every  case  was  at  the  same  distance  from  the  objective. 
Variations  of  an  abnormal  character  in  the  diameters  of  the 
stellar  images  on  the  different  plates  could  now  be  attributed 
to  varying  sensitiveness  of  these  plates,  as  the  atmospheric 
conditions  were  practically  the  same  for  all  the  plates  exposed 
on  any  given  day.  The  tabular  data  and  results  are  arranged 
as  in  the  previous  observations,  and  therefore  require  no 
further  explanation. 


The  Photographic  Rays  of  Light. 


U.  S.  N.  0.  Telescope.                a  Andromedae.                                Bar.,  25">.95. 

July  1,  1890.                                                                                                     Att.,  64°.5. 

Plate  No.  1.                                     TABLE  XIX.                                    Ex.,  63°.0. 

d 

T 

r 

c 

2s 
4s 
8" 

Q 

Mean 
Q 

o  —  c 

171l34m 

_6h29m 

78°.4 

55 
60 

0.65 
0.60 

0.65 

—  0.06 

70 

0.70 

60 

0.80 

17    49                  6    14 

76  .1 

65 

0.70 

0.77 

+  0.01 

75 

0.80 

60 

0.80 

17   57 

6     1 

74  .0 

70 

0.85 

0.85 

+  0.05 

80 

0.90 

65 

1.00 

18    39 

5    24 

66  .5 

70 

0.85 

0.92 

+  0.01 

80 

0.90 

65 

1.00 

19     5 

4   58 

61  .6 

75 

1.00 

1.00 

+  0.03 

85 

1.00 

65 

1.00 

19   45 

4    18 

54  .0 

75 

1.00 

0.97 

—  0.08 

80 

0.90 

70 

1.20 

20    11 

3    52 

48  .7 

80 

1.20 

1.13 

+  0.04 

85 

1.10 

70 

1.20 

20   36 

3    27 

43  .8 

75 

1.00 

1.10 

—  0.02 

90 

1.10 

70 

1.20 

20   49 

3    14 

41  .3 

80 

1.20 

1.17 

+  0.03 

90 

1.10 

Equations  of  Condition. 

a  —  0.92  /?  =  0.65  a  —  0.50  (3  =  1.00 

a  —  0.84  ft  =  0.77  a  —  0.37  ft  =  0.97 

a  —  0.78  fi  =  0.85  a  —  0.30  /?  =  1.13     (71) 

a  —  0.59  ft  =  0.92  a  —  0.24  /3  =  1.10 

a  —  0.21  /5  =  1.22 


Normal  Equations. 

9.00^  —  4.75/3  =  8.56 
4.75  or  — 3.10/3  =  4.16 

Solution  of  Normals. 

<x=  1.273 

?  =  0.608 


(72) 


(73) 


40 


Terrestrial  Atmospheric  Absorption  of 


U.  S.  N.  0.  Telescope.              a  Andromedae.                            Bar-.  25in-95. 

July  1,  1890.                                                                                                    Att.,  64°. 

Plate  No.  2.                                      TABLE  XX.                                   Ex.,  63°. 

T 

r 

C 

d 

Q 

Mean 
Q 

o—c 

55 

0.65 

17"  24" 

—  6"  39" 

80°.2 

60 

0.60 

0.62 

—  0.10 

65 

0.60 

60 

0.80 

17   39 

6   24 

77.5 

65 

0.70 

0.77 

0.00 

70 

0.70 

60 

0.80 

17   44 

6    19 

76.6 

70 

0.85 

0.82 

+  0.04 

75 

0.80 

60 

0.80 

18     1 

6     2 

73  .6 

70 

0.85 

0.85 

—  0.02 

80 

0.90 

65 

1.00 

18   34 

5   29 

67  .4 

75 

1.00 

1.00 

+  0.10 

85 

LOO 

65 

1.00 

19    11 

4    52 

60.5 

75 

1.00 

1.00 

+  0.03 

85 

1.00 

65 

1.00 

19   41 

4    22 

54  .6 

75 

1.00 

1.00 

—  0.02 

85 

1.00 

65 

1.00 

20   20 

3   43 

46  .9 

75 

1.00 

1.03 

—  0.04 

90 

1.10 

70 

1.20 

20   54 

3     9 

40.3 

75 

1.00 

1.07 

—  0.03 

85 

1.00 

21   21 

2   42 

34  .9 

65 
80 

1.00 
1.20 

1.10 

—  0.03 

90 

L10 

Equations  of  Condition. 
a  —  0.99/3  =  0.62  a  —  0.47  /3  =  1 .00 

a  —  0.89/5=0.77  a  —  0.38  /3=  1.00 

a  —  0.86/3  =  0.82  a-  0.27  /3  =  1.03     (74) 

a  —  0.77^  =  0.85  a  —  0.20  /3  =  1.07 

a  —  0.62  /?=  1.00  a  —  0.15/5=1.10 

Normal  Equations. 

10.00  a  —  5.60/5  =  9.26  (75) 

5.60  a  —  3.97  /?  =  4.78 

Solution  of  Normals. 

a  =  1.196  (76) 

ft  =  0.483 


The  Photographic  Rays  of  Light. 


41 


U.  S.  N.  O.  Telescope. 
July  2,  1890. 
Plate  No.  1. 


a  Andromedae. 
TABLE  XXI. 


Bar.,  25'°.90. 
Att.,  64°. 
Ex.,  63°. 


T 

T 

C 

d 

Q 

Mean 
Q 

o  —  c 

60 

0.80 

17h  8m 

—  6h  65m 

83°.2 

0.85 

—  0.03 

80 

0.90 

65 

LOO 

17  29 

6  34 

79.4 

75 

1.00 

1.00 

+  0.04 

70 

1.20 

18  10 

5  53 

71  .9 

75 

1.00 

1.10 

+  0.01 

90 

1.10 

19  9 

4  54 

60  .9 

70 

1.20 

1.20 

—  0.02 

75 

1.45 

20  20 

3  43 

46  .9 

85 

1.30 

1.33 

0.00 

95 

1.25 

Equations  of  Condition. 

a  —  1.18/5  =  0.85 
of  —  0.96  /?  =  1.00 
a  —  0.72/5=1.10 
a  —  0.48  /3  =  1.20 
a  —  0.27  ft  =  1.33 

Normal  Equations. 

5.00  a  —  3.54  /?=  5.48 
3.54  «  — 2.97/5  =  3.63 

Solution  of  Normals. 

or  =1.480 
/5  =  0.542 


(77) 


(78) 


(79) 


42  Terrestrial  Atmospheric  Absorption  of 


r.s.  X.  0.  Telescope. 
July  2, 1890. 


a  Andromedae. 
TABLE  XXII. 


Plate  Xo.  2. 


T 

r 

r 

d 

Q 

Mean 
Q 

o—  c 

55 

0.65 

lyh  12111 

—  6"  51°> 

82°.4 

0.65 

—  0.04 

60 

0.80 

17   32 

6   31 

78  .8 

65 

0.70 

0.77 

+  0.01 

75 

0.80 

65 

1.00 

18    14 

5   49 

71  .1 

0.95 

+  0.07 

80 

0.90 

65 

1.00 

19   13 

4   50 

60.1 

75 
85 

1.00 
1.00 

1.00 

+  0.01 

65 

1.00 

20   23 

3   40 

46.3 

75 

1.00 

1.03 

—  0.06 

90 

1.10 

Equations  of  Condition. 
a—  1.08  /3  =  0.65 
a  —  0.94/5  =  0.77 
«  —  0.70  /5  =  0.95 
a  —  0.47/5=1.00 
«r  —  0.27  /S  =  1.03 

Normal  Equations. 

5.00  a  — 3.46 /?  =  4.40 
3.46  a  —  2.83/5  =  2.83 

Solution  of  Normals. 

a=  1.220 
/?=  0.492 


(80) 


(81) 


(82) 


The  Photographic  Rays  of  Light. 


43 


I".  S.  X.  O.  Telescope. 
July  2,  1890. 


a  Andromedae. 
TABLE  XXIII. 


Plate  No.  3. 


T 

r 

' 

d 

Q 

Mean 
Q 

o  —  c 

55 

0.65 

17"  16" 

—  6M7m 

81°.6 

65 

0.70 

0.72 

—  0.12 

75 

0.80 

65 

LOO 

17    36 

6   27 

78.1 

75 

1.00 

1.00 

+  0.08 

85 

1.00 

70 

1.20 

18     9 

5   54 

72  .1 

80 

1.20 

1.13 

+  0.11 

85 

1.00 

70 

1.20 

19    16 

4   47 

59  .5 

80 

1.20 

1.18 

+  0.01 

90 

1.15 

70 

1.20 

20   34 

3    29 

44  .2 

80 

1.20 

1.22 

—  0.07 

95 

1.25 

Equations  of  Condition, 
a  —  1.04  p  =  0.72 
a  — 0.91 /?  =  1.00 
a  —  0.73/3  =  1.13 
a  —  0.46^  =  1.18 
a  —  0.24  ft  =  1.22 

Normal  Equations. 

5.00  a  —  3.38/5  =  5.25 
3.38  or  —  2.71  ft  =  3.31 

Solution  of  Normals. 

a  =  1.431 
/?  =  0.564 


(83) 


(84) 


(85) 


44 


Terrestrial  Atmospheric  Absorption  of 


U.  S.  N.  O.  Telescope. 
July  2, 1890. 


a  Andromedae. 
TABLE  XXIV. 


Plate  No.  4. 


T 

r 

e 

d 

Q 

Mean 
Q 

o  —  c 

60 

0.80 

17h  20"» 

—  6"43» 

81°.0 

70 

0.85 

0.82 

—  0.03 

65 

1.00 

17  39 

6  24 

77  .5 

75 

80 

1.00 
0.90 

0.97 

+  0.04 

65 

1.00 

18  19 

5  44 

70.2 

80 
90 

L15 
1.10 

1.08 

+  0.02 

70 

1.20 

19  19 

4  44 

58  .9 

80 

1.20 

1.17 

—  0.04 

90 

1.10 

75 

1.45 

20  39 

3  24 

43  .2 

85 
100 

1.30 
1.35 

1.37 

+  0.02 

Equations  of  Condition. 

a—  1.02  p  =  0.82 
a  —  0.89  ft  =  0.97 
a  —  0.68  fi  =  1.08 
a  —  0.45  p  =  1.17 
a  — 0.23/3  =  1.37 

Normal  Equations. 

5.00  a  —  3.27  /?=  5.41 
3.27  «  —  2.54/5  =  3.28 

Solution  of  Normals. 

a  =1.502 

/?  =  0.642 


(86) 


(87) 


(88) 


The  Photographic  Rays  of  Light. 


45 


r.  S.  X.  0.  Telescope. 
July  2,  1890. 


a  Andromedae. 
TABLE  XXV. 


Plate  Xo.  5. 


r 

r 

c 

d 

Q 

Mean 
Q 

o—  c 

17*24* 

—  6"  39-° 

80°.2 

60 
70 

0.80 
0.85 

0.82 

—  0.03 

17  42 

6  21 

77  .0 

65 

1.00 

0.95 

+  0.04 

18  22 

5  41 

69  .7 

80 
65 

0.90 
1.00 

1.00 

0.00 

19  22 
20  46 

4  41 
3  17 

58  .3 
41  .1 

85 

70 
80 
90 

70 
85 
90 

1.00 

1.20 
1.15 
1.10 

1.20 
1.30 
1.10 

1.15 
1.20 

+  0.04 
—  0.02 

Equations  of  Condition. 

a  —  0.99/5  =  0.82 
a  —  0.87/5  =  0.95 
a  — 0.67/3=  1.00 
a  —  0.44/3=1.15 
a  — 0.21  £=1.20 

Normal  Equations. 

5.00  a  —  3.18/5=5.12 
3.1 8  a  — 2.42/5  =  3.07 

Solution  of  Normals. 

a =1.323 

/5  =  0.472 


(89) 


(90) 


(91) 


46 


Terrestrial  Atmospheric  Absorption  of 


U.  S.  N.  0.  Telescope. 
July  30, 1890. 
Plate  No.  1. 


a  Andromedae. 

TABLE  XXVI. 


Bar.,  25K86. 
Att.,  67°. 
Ex.,  65°. 


r 

T 

c 

d 

Q 

Mean 
Q 

o  —  c 

55 

0.65 

17»  31«> 

—  6»32'» 

79°.0 

65 

0.70 

0.72 

—  0.08 

75 

0.80 

60 

0.80 

17  47 

6  23 

77  .3 

0.85 

—  0.01 

80 

0.90 

65 

1.00 

18  5 

5  58 

72  .8 

75 

1.00 

1.00 

+  0.07 

70 

1.20 

19  21 

4  42 

58  .5 

80 

1.20 

1.18 

+  0.07 

90 

1.15 

( 

70 

1.20 

20  52 

3  11 

40  .7 

1.22 

—  0.04 

95 

1.25 

70 

1.20 

21  48 

2  15 

29  .5 

90 

1.45 

1.30 

—  0.03 

95 

1.25 

Equations  of  Condition. 

a  —  0.94/5  =  0.72 
a  —  0.84  ft  =  0.85 
a  —  0.74/5=1.00 
a  —  0.44  /3  =  1.18 
a  —  0.21  ytf  =  1.22 
a  —  0.10/5=1.30 

Normal  Equations. 

6.00  «  — 3.27/5  =  6.27 
3.27  a  —  2.38  /5  =  3.04 

Solution  of  Normals. 

a=  1.387 
/5  =  0.628 


(92) 


(93) 


(94) 


The  Photographic  Rays  of  Light. 


47 


U.  S.  N.  0.  Telescope. 
July  30, 1890. 


a  Andromedae. 
TABLE  XXVII. 


Plate  No.  2. 


T 

r 

c 

- 

Q 

Mean 
Q 

o  —  c 

60 

0.80 

17h  34m 

—  6h  29m 

78°.4 

70 

0.85 

0.82 

—  0.05 

75 

0.80 

65 

1.00 

17  50 

6  13 

75  .5 

75 

1.00 

0.97 

+  0.05 

80 

0.90 

60 

0.80 

18  7 

5  56 

72  .4 

75 

1.00 

0.93 

—  0.03 

85 

1.00 

70 

1.20 

19  23 

4  40 

58  .1 

80 
90 

1.20 
1.10 

1.17 

+  0.06 

70 

1.20 

20  56 

3  7 

39.9 

80 

1.20 

1.22 

—  0.01 

95 

1.25 

70 

1.20 

21  54 

2  9 

28  .3 

85 

1.30 

1.25 

—  0.02 

95 

1.25 

70 

1.20 

22  24 

1  39 

22  .5 

1.27 

—  0.02 

1.00 

1.35 

Equations  of  Condition. 

a  —  0.92  /5  =  0.82 
a  —  0.83  /5  =  0.97 
a  —  0.74/5  =  0.93 
a  —  0.43  /5  =  1.17 
«— 0.19  y3  =  1.22 
or  — 0.10/5=1.25 
«  —  0.06/5=1.27 

Normal  Equations. 

7.00  or  — 3.27/5=7.63 
3.27  a—  2.32/5=3.18 

Solution  of  Normals. 
a=  1.317 
/?  =  0.486 


(95) 


(96) 


(97) 


48  Terrestrial  Atmospheric  Absorption  of 


U.  S.  N.  O.  Telescope. 
July  30,  1890. 


a.  Andromedae. 
TABLE  XXVIII. 


Plate  No.  3. 


T 

r 

c 

d 

Q 

Mean 
Q 

o  —  c 

17"  38«> 
17  52 
18  10 
19  26 

_6n  25" 
6  11 
5  53 
4  37 

77°.7 
75  .2 
71  .9 
57  .5 

65 
75 
85 

70 
80 
90 

75 
85 
95 

80 

1.00 
1.00 
1.00 

1.20 
1.20 
L10 

1.40 
1.30 
L25 

1.70 

1.00 
1.17 
1.32 
1.52 

—  0.07 
—  0.01 
+  0.08- 
+  0.10 

20  59 

3  4 

39  .3 

100 

80 
90 

1.35 

1.70 
1.50 

1.60 

+  0.04 

21  57 

2  6 

27  .7 

80 
90 

1.70 
1.50 

1.60 

—  0.02 

22  27 

1  36 

21  .9 

95 

110 

1.65 
1.60 

1.62 

—  0.08 

Equations  of  Condition, 
a  —  0.90  /3  =  1.00 
a  —  0.82/3  =  1.17 
a  —  0.72/5=1.32 
a  —  0.42  /3  =  1.52 
a  —  0.19  /3  =  1.60 
a  —  0.09  ft  =  1.60 
a  —  0.06/5  =  1.62 

Normal  Equations. 

7.00  or  — 3.20/5  =  9.83 
3.20  a  —  2.23  /5  =  3.99 

Solution  of  Normals, 
a  =  1.703 
/?=  0.654 


(98) 


(99) 


(100) 


The  Photographic  Rays  of  Light. 


U.  S.  N.  0.  Telescope. 
July  30,  1890. 


a  Andromedae. 
TABLE  XXIX. 


49 


Plate  No.  4. 


T 

r 

c 

d 

Q 

Mean 
Q 

o—  c 

17h  41™ 

—  6h  22™ 

77°.2 

60 
70 

80 

0.80 
0.85 
0.90 

0.85 

—  0.07 

17  54 
18  12 
19  29 

6  9 
5  51 
4  34 

74.8 
71  .5 
56  .9 

70 

85 

65 
75 
90 

70 
80 
95 

0.85 
1.00 

1.00 
1.00 
1.10 

1.20 
1.20 
1.25 

0.92 
L03 
1.22 

—  0.04 
+  0.03 
+  0.07 

21  1 

3  2 

38  .9 

80 

1.20 

1.20 

—  0.06 

22  0 

2  3 

27  .1 

85 

1.30 

1.30 

—  0.01 

Equations  of  Condition. 

«  — 0.88/3  =  0.85 
a  —  0.80  ft  =  0.92 
a  — 0.71  /3  =  1.03 
a  — 0.41  0  =  1.22 
a—  0.19/3=1.20 
a  —  0.09/5=1.30 

Normal  Equations. 

6.00  a  —  3.08/3  =  6.52 
3.08  a  —  2.13/3  =  3.07 

Solution  of  Normals. 

a  =1.359 
/3  =  0.503 


(101) 


(102) 


(103) 


50  Terrestrial  Atmospheric  Absorption  of 


V .  s.  N.  O.  Telescope. 
July  30, 1890. 


x  Andromedae. 
TABLE  XXX. 


Plate  No.  5. 


r 

r 

c 

d 

Q 

Mean 
Q 

o  —  c 

17"  44"' 

—  6h  19m 

76°.6 

60 
70 
80 

0.80 
0.85 
0.90 

0.85 

—  0.11 

17  56 

6  7 

74  .4 

65 

1.00 

1.00 

-f-001 

18  14 

5  49 

71  .1 

70 
80 
90 

1.20 
1.20 
1.10 

1.17 

-fO.13 

19  32 

4  31 

56  .4 

70 
80 
95 

1.20 
1.20 
1.25 

1.22 

+0.04 

21  4 

2  59 

38  .3 

70 
85 
95 

1.20 
1.30 
1.25 

1.25 

—  0.05 

22  3 

2  0 

26.5 

75 
85 

1.40 
1.30 

1.35 

0.00 

Equations  of  Condition. 

a  —  0.86  ft  =  0.85 
«  — 0.79/3  =  1.00 

a  —  0.70/5  =  1.17 
a  —  0.41/5=1.22 
a  —  0.18/5  =  1.25 
a  — 0.08 /?  =  1.35 

Normal  Equations. 

6.00  a-— 3.02/5=6.84 
3.02  a  —  2.06/5=3.17 

Solution  of  Normals. 

a  =1.393 
/5  =  0.503 


(104) 


(105) 


(106) 


The  Photographic  Rays  of  Light. 


51 


U.  S.  X.  ().  Telescope.                a  Andromedae.                                 Bar.,  26i".04. 
August  6,  1890.                                                                                                Att..  69°. 
Plate  No.  1.                                  TABLE  XXXI.                                   Ex-)  6go 

T 

T 

c 

d 

Q 

Mean 
Q 

o  —  c 

I7h  44m 

_6h   19m 

76°.6 

60 

75 
85 

0.80 
1.00 
1.00 

0.93 

—  0.02 

18    32 

5    31 

(37  .8 

70 
80 
90 

1.20 
1.20 
1.10 

1.17 

+  0.04 

19    29 

4    34 

57  .0 

70 
85 
95 

1.20 
1.30 
1.35 

1.25 

—  0.03 

Equations  of  Condition. 

^_0.86yS  =  0.93 
or  — 0.62  0=1.17 
a  —  0.42  /?=  1.25 

Normal  Equations. 

3.00  a  —  1.90  j3=  3.35 
1.90  a— 1.30/J  =  2.05 

Solution  of  Normals. 

a=  1.589 
ft  =  0.745 


(107) 


(108) 


(109) 


Terrestrial  Atmospheric  Absorption  of 


1".  s.  X.  O.  Telescope. 
August  6, 1890. 


of  Andromedae . 
TABLE  XXX II. 


Plate  No.  2. 


T 

r 

r 

' 

Q 

Mean 
Q 

o  —  c 

65 

1.00 

17*1  47m 

—  6"  16m           76°.0               70 

0.85 

0.92  !        —  0.02 

80 

0.90 

70 

1.20 

18   34 

5   29 

67  .4 

80 
90 

1.20 
1.10 

L17 

4-0.07 

70 

1.20 

19   32 

4    31              56  .4               85 

1.30  i           1.20 

—  0.05 

90 

1.10 

Equations  of  Condition. 

a  —  0.84  /?  =  0.92 
a  —  0.61/5  =  1.17 
a  — 0.41 /?  =  1.20 

Normal  Equations. 

3.00  a—  1.86  yff  =  3.29 
1.86  a  — 1.25 /?  =  1.97 

Solution  of  Normals. 

a=  1.550 
/?  =  0.731 


(110) 


(111) 


(112) 


The  Photographic  Rays  of  Light. 


u.  s.  N.  0.  Telescope.              «  Andromedae.                         Poor  focus. 

August  6,  1890.                           TABLE    XXXIII.                               Plate  No.  3. 

T 

T 

C 

d 

Q 

Mean 
Q 

o  —  c 

17"  50'» 

—  6"  13-" 

75°.5 

65 
70 
80 

1.00 
0.85 
0.90 

0.92 

+  0.01 

18   37 

5   26 

66  .8 

70 
80 
90 

1.20 
1.20 
1.10 

1.17 

+  0.02 

19   34 

4    29 

56  .0 

70 
80 
95 

1.20 
1.20 
1.25 

1.22 

-0.03 

Equations  of  Condition. 

a  —  0.83  /3  =  0.92 
a  —  0.60/5  —  1.17 
,r_  0.40/?  =  1.22 

Normal  Equations. 

3.00  or  —  1.83  /?  =  3.31 
1.83  or  —  1.21  /?  =  1.95 

Solution  of  Normals. 

a  =1.545 

ft  =  0.725 


(113) 


(114) 


(115) 


54 


Terrestrial  Atmospheric  Absorption  of 


V .  S.  N.  O.  Telescope. 
August  6,  1890. 


a  Andromedae. 
TABLE   XXXIV. 


Plate  No.  4. 


T 

r 

c 

d 

Q 

Mean 
Q 

o—c 

65 

1.00 

17h  52"' 

—  6h  llm 

75°.2 

1.00 

+  001 

85 

1.00 

70 

1.20 

18   40 

5    23 

66  .3 

80 
90 

1.20 
1.10 

1.17 

+  0.02 

70 

1.20 

19   37 

4   26 

55  .0 

85 

1.30 

1.25 

—  0.04 

95 

1.25 

Equations  of  Condition. 

a  —  0.82  ft=  1.00 
a  —  0.59  yS  =1.17 
cc  —  0.38  /3=  1.25 

Normal  Equations. 
3.00  a—  1.79/5  =  3.42 
1.79  a  — 1.16/5  =  1.98 

Solution  of  Normals. 

a  =1.538 
/9  =  0.667 


(116) 


(117) 


(118) 


The  Photographic  Rays  of  Light. 


55 


U.  S.  N.  0.  Telescope. 
August  6,  1890. 


of  Andromedae. 
TABLE  XXXV. 


Plate  No.  5. 


T 

r 

c 

d 

Q 

Mean 
Q 

o  —  c 

60 

0.80 

ITU  54m 

—  6"  9»' 

74°.8 

70 

0.85 

0.85 

+  0.01 

80 

0.90 

65 

1.00 

18  42 

5  21 

66.0 

75 

1.00 

1.00 

0.00 

85 

1.00 

70 

1.20 

19  39 

4  24 

55.0 

80 

1.20 

1.13 

—  0.02 

85 

1.00 

Equations  of  Condition. 

a  —  0.80  /3  =  0.85 
a  —  0.58  /3  =  1.00 
a  —  0.38  /3=  1.03 

Normal  Equations. 

3.00  a— 1.76/?  =  2.88 
1.76  a  — 1.12  /?=1.65 

Solution  of  Normals. 

a=  1.235 
/?  =  0.469 


(119) 


(120) 


(121) 


56  Terrestrial  Atmospheric  Absorption  of 


U.  s.  X.  0.  Telescope.              a  Andromedae.                            Bar.,  25»>.85. 
August  12,  1890.                                                                                              Att.,  69°. 
Plate  Xo.  1.                                 TABLE  XXXVI.                                Ex,  67°. 

T 

T 

:           d          q 

Mean 
Q 

17h56» 
18   32 
21   50 
22   60 

—  6"    7m 
5   31 
2   13 
1   13 

74°.3 

67  .8 
29  .1 
17  .8 

0.75          —  0.07 
1.00          +0.08 
1.25          +0.03 
1.22          —0.04 

65 

75 

65 

75 

0.70 
0.80 

1.00 
1.00 

95 

1.25 

70 
80 
95 

1.20 
1.20 
1.25 

Equations  of  Condition. 

a  —  0.79/6  =  0.75 
a  —  0.62  0  =  1.00 
a  —  0.10  /3  =  1.25 
a  —  0.04/5  =  1.22 

Normal  Equations. 
4.00  a  —  1.55  ft  =  4.22 
1.55  a  — 1.04/5  =  1.38 

Solution  of  Normals. 
a=  1.280 
0  =  0.581 


(122) 


(123) 


(124) 


The  Photographic  Rays  of  Light. 


57 


U.  S.  N.  0.  Telescope. 
August  12, 1890. 


a  Andromedae. 
TABLE  XXXVII. 


Plate  No.  2. 


r 

r 

c 

d 

Q 

Mean 
Q 

o  —  c 

17"  59" 

_6h  4m 

73°  .6 

60 
70 

80 

0.80 
0.85 
0.90 

0.85 

—  0.04 

18  34 

5  29 

67  .4 

75 

1.00 

1.00 

+  0.04 

19  29 

4  34 

57  .0 

90 

1.10 

1.10 

—  0.03 

20  45 

3  18 

41  .6 

80 

1.20 

1.20 

+  0.02 

21  53 

2  10 

28  .5 

80 

1.20 

1.20 

—  0.04 

22  52 

1  11 

17  .5 

1.25 

—  0.02 

95 

1.25 

Equations  of  Condition. 

a  —  0.77/5  =  0.85 
a  — 0.62/3  =  1.00 
a  —  0.42/5=1.10 
a  — 0.21/3  =  1.20 
«_  0.10/5  =1.20 


Normal  Equations. 

6.00  a  —  2.15/5=6.60 
2.15  a  —  1.20/5  =  2.14 

Solution  of  Normals. 

a- =1.288 
A  =  0.525 


(125) 


(126) 


(127) 


58  Terrestrial  Atmospheric  Absorption  of 


\  .  -    N .  o.  Telescope. 
August  12, 1890. 


a  Andromedae. 
TABLE   XXXVIII. 


Plate  No.  3. 


r 

T 

r 

•; 

d 

Q 

Mean 
Q 

o—c 

18"    1"> 

_6h    2"> 

73°.4 

60 
70 
80 

0.80 
0.85 
0.90 

0.85 

-0.03 

18   36 

5    27 

67  .0 

1.00 

0.00 

19   32 

4   31 

56  4 

85 
70 

1.00 
1.20 

120 

+006 

20   48 

3    15 

41  .5 

85 

1.30 

1.30 

+  0.01 

21   55 

2     8 

28  .1 

75 
85 
95 

1,45 
1.30 
1.25 

1.33 

—  0.04 

Equations  of  Condition. 

a  —  0.76/5  =  0.85 
a  —  0.60  /?  =  1.00 
or—  0.41  /?  =  1.20 
a  —  0.21  /3=1.30 
a  —  0.09/5  =  1.33 

Normal  Equations. 

5.00  a  —  2.07/5=5.68 
2.07a  —  1.16  /?  =  2. 


Solution  of  Normals. 

«=  1.439 
/?  =  0.733 


(128) 


(129) 


(130) 


The  Photographic  Rays  of  Light. 


59 


U.  S.  N.  O.  Telescope. 
August  12,  1890. 


(x  Andromedae. 
TABLE  XXXIX. 


Plate  No.  4. 


r 

r 

- 

d 

Q 

Mean 
Q 

o  —  c 

65 

1.00 

18"  4m 

—  5"  59°> 

73°  .0 

75 

1.00 

1.00 

—  0.04 

85 

1.00 

70 

1.20 

18  39 

5  24 

66  .5 

80 

1.20 

1.17 

+  0.04 

90 

1.10 

70 

1.20 

19  35 

4  28 

55  .8 

85 

1.30 

1.25 

+  0.02 

95 

1.25 

75 

1.45 

20  51 

3  12 

40  .9 

85 

1.30 

1.37 

+  0.03 

95 

1.35 

21  58 

2  5 

27  .5 

1.35 

—  .05 

100 

1.35 

Equations  of  Condition. 
a  —  0.75  /3  =1.00 
a  —  0.59/5=1.17 
a  —  0.40  /3=  1.25 
a  —  0.20  /3=  1.37 
a  —  0.09  ft=  1.35 

Normal  Equations. 

5.00  a  —  2.03  fi  =  6.14 
2.03  «  —  1.12  yS  = 


(131) 


(132) 


Solution  of  Normals. 


=  0.548 


(133) 


60  Terrestrial  Atmospheric  Absorption  of 


r.  s.  N.O.  Telescope. 
August  12, 1890. 


of  Andromedae. 
TABLE  XL. 


Plate  No.  5. 


r 

T 

c 

d 

Q 

Mean 
Q 

o  —  c 

I8h     7m 

—  5^56" 

72°.5 

60 
65 

75 

0.80 
0.70 
0.80 

0.77 

—  0.01 

18   41 

5   22 

66  .2 

70 

0.85 

0.85 

+  0.01 

20   54 

3     9 

40  .3 

L10 

+  001 

22     1 

2     2 

26  .9 

90 
70 

L10 

1.20 

L20 

+  003 

23     2 

1     1 

15  .8 

80 
95 

L15 
1.25 

1.20 

—  0.01 

Equations  of  Condition. 

a  —  0.59/5  =  0.77 
a  —  0.51  /3  =  0.85 
«  —  0.19  /S  =  1.10 
a  —  0.09/5  =  1.20 
a  — 0.03/5  =  1.20 

Normal  Equations. 

5.00  or— 1.41/3=5.12 
1.41  a  —  0.66/3=1. 24 

Solution  of  Normals. 

a  =1.244 
/?  =  0.780 


(134) 


(135) 


(136) 


The  Photographic  Rays  of  Light. 


61 


U.  S.  X.  O.  Telescope. 
August  13, 1890. 
Plate  No.  1. 


a.  Andromedae. 
TABLE  XLI. 


Bar.,  25'° 
Att.,  65°. 
Ex.,  64°. 


T 

T 

^ 

d 

Q 

Mean 
Q 

o  —  c 

17h28'« 

—  6i  35" 

79°.5 

60 
70 

0.80 

0.85 

0.82 

—  0.02 

65 

1.00 

18  22 

5  41 

69  .7 

1.00 

+  0.01 

85 

1.00 

70 

1.20 

19  45 

4  18 

53  .8 

80 

1.20 

1.17 

+  0.04 

90 

1.10 

70 

1.20 

21  0 

3  3 

39  .1 

85 

1.30 

1.25 

+  0.03 

95 

1.25 

70 

1.20 

22  29 

1  34 

21  .6 

85 

1.30 

1.25 

—  0.03 

95 

1.25 

Equations  of  Condition. 

a  —  0.96/5  =  0.82 
a  —  Q.67/5  =  1.00 
'a  —  0.37,3  =  1.17 
a  —  0.19/5  =  1.25 
<*  — 0.06/5  =  1.25 

Normal  Equations. 

5.00  a  —  2.25  /?  =  5.49 
2.25  a  —  1.55/5  =  2.21 

Solution  of  Normals. 

a  =  1.314 

/5  =  0.485 


(137) 


(138) 


(139) 


62  Terrestrial  Atmospheric  Absorption  of 


U.S.  \ .  O.  Telescope. 
August  13,  1890. 


a  Andromedae. 
TABLE  XLTI. 


Plate  Xo.  2 


T 

r 

C 

d 

2> 
4* 
8s 

Q 

Mean 
Q 

o—  c 

. 

0.80 

17h  31m 

6h  32" 

79°  0 

080 

-  001 

65 

1.00 

18  35 

5  28 

67  .2 

75 

1.00 

1.00 

+  0.01 

70 

1.20 

19  47 

4  16 

53  .4 

80 
90 

1.20 
1.15 

1.17 

+  0.04 

70 

1.20 

21  5 

2  58 

38  .1 

80 

1.20 

1.22 

0.00 

95 

1.25 

70 

1.20 

22  32 

1  31 

21  .0 

85 

1.30 

1.25 

-0.04 

95 

1.25 

Equations  of  Condition. 

a  —  0.94/5  =  0.80 
a  — 0.61  ,5  =  1.00 
a  —  0.36/5=1.17 
ex  —  0.18/5=1.22 
a  —  0.05/5=1.25 

Normal  Equations. 

5.00^  —  2.14/5  =  5.44 
2.1 4  a  — 1.41  /5  =  2.06 

Solution  of  Normals. 

or  =  1.320 

0  =  0.541 


(140) 


(141) 


(142) 


The  Photographic  Rays  of  Light. 


63 


U.  S.  N.  0.  Telescope. 
August  13, 1890. 


a  Andromedae. 
TABLE  XLIII. 


Plate  No.  3. 


T 

r 

c 

d 

Q 

Mean 
Q 

o  —  c 

17h  33m 

—  6h  30" 

78°  .6 

65 

1.00 

1.00 

+  0.05 

18  37 

5  26 

66  .9 

75 
85 
95 

1.45 
1.30 
1.25 

1.33 

—  0.03 

19  50 

4  13 

52  .8 

80 
90 

1.70 
1.50 

1.60 

—  0.08 

21  10 

2  53 

37  .1 

90 
100 
120 

2.30 
1.80 
1.85 

1.98 

+  0.07 

22  35 

1  28 

20  .4 

90 
105 
120 

2.30 
2.00 
1.85 

2.05 

—  0.01 

Equations  of  Condition. 

a  —  0.93 /?=  1.00 
«  — 0.60 /?=  1.33 
a  —  0.35  ft=  1.60 
a  —  0.17/5=1.98 
a  —  0.05/3  =  2.05 

Normal  Equations. 

5.00  a  —  2.10  /?  =  7.96 
2.100'—  1.37/5=2.73 

Solution  of  Normals. 
a=  2.121 
/?==  1.259 


(143) 


(144) 


(145) 


64 


Terrestrial  Atmospheric  Absorption  of 


V .  s.  X.  O.  Telescope. 
August  13, 1890. 


a  Andromedae. 
TABLE  XLIV. 


Plate  No.  4. 


r 

r 

c 

d 

Q 

Mean 

Q 

o  —  c 

0.65 

1.00 

17"  36" 

—6"  28- 

78°.2 

0.60 

0.60 

0.80 

—  0.09 

0.70 

1.20 

18   39 

5   24 

66  .5 

0.80 

1.20 

1.17 

+  0.08 

0.90 

1.10 

0.75 

1.40 

19   52 

4    11 

52.6 

0.80 

1.20 

1.28 

+  0.06 

0.95 

L25 

0.75 

1.40 

21   15 

2   48 

36  .1 

0.85 

1.30 

1.32 

—  0.02 

0.95 

1.25 

0.75 

1.40 

22   37 

1   26 

20.0 

0.85 

1.30 

1.35 

—  0.05 

1.00 

1.35 

Equations  of  Condition. 

a  —  0.92  /3  =  0.80 
a  —  0.59 /?=  1.17 
a  —  0.35/5=1.28 
a  —  0.16/3=1.32 
a  —  0.05  /S=1.35 

Normal  Equations. 

5.00  «  —  2.07  ytf=5.92 
2.07  a  — 1.35/3  =  2.16 

Solution  of  Normals. 

a  =  1.429 
yff  =  0.592 


(146) 


(147) 


(148) 


TJie  Photographic  Rays  of  Light, 


65 


U.  S.  N.  O.  Telescope. 
August  13,  1890. 


a.  Andromedae. 
TABLE  XLY. 


Plate  No.  5. 


r 

T 

c 

d 
2 
4 
8 

Q 

Mean 
Q 

o—  c 

60 

0.80 

17"  38" 

—  6»25m 

77°  .7 

65 

0.70 

0.75 

0.00 

65 

1.00 

18    41 

5    22 

66.2 

70 

0.85 

0.92 

+  0.01 

80 

0.90 

65 

1.00 

19    55 

4     8 

51.8 

75 

1.00 

1.03 

-0.02 

90 

L10 

21    20 

2   43 

35  .1 

70 

80 

1.20 
1.20 

1.17 

+  0.02 

90 

1.10 

70 

1.20 

22    39 

1    24 

19.7 

80 

1.20 

1.17 

—  0.03 

90 

1.10 

Equations  of  Condition. 

a  —  0.90/5  =  0.75 
a  —  0.59/5  =  0.92 
a  —  0.34,5  =  1.03 
a  —  0.15/5=1.17 
tf  — 0.05/5=1.17 

Normal  Equations. 

5.00  a  —  2.03/5=5.04 
2.03  a— 1.30/5=1.79 

Solution  of  Normals. 

a=  1.226 
p  =  0.536 


(149) 


(150) 


(151) 


66 


Terrestrial  Atmospheric  Absorption  of 


Exposures  on  Polaris. 

In  addition  to  the  observations  on  a  Andromedae  each  plate 
was  exposed  on  Polaris;  ordinarily  one  set  of  2",  4s,  and  8s  ex- 
posures was  made  on  each  plate  at  the  beginning  of  the  night's 
work,  and  a  similar  set  at  the  close.  The  observations  and 
results  are  given  in  Table  XL VI.  The  last  column  gives  the 
quantity  (expressed  in  magnitudes),  found  by  subtracting  the 
provisional  magnitude  of  a  Andromedae  from  that  of  Polaris. 
(See  note  to  Table  VIII.) 

TABLE  XLVI. 


Polaris. 

Q 

1 
mf 

i      f 

Date. 

Plate. 

d 

Q 

Polaris. 

a 

Andro. 

Polaris. 

a 
Andro.  \ 

1890. 

65 

II 
1.00  ;1 

July     1.. 

1 

70 

0.85 

0.88 

1.25 

2.28 

1.52     +0.76 

75 

0.80 

65    65 

1.00 

July     I.- 

2 

70    70 

0.85 

0.88 

1.20 

2.28 

1.61     +  0.67 

75    75 

0.80 

65    65 

1.00 

July     2.. 

1 

70    70 

0.85 

0.88 

1.48 

2.28 

1.15     +  1.13 

75    75 

0.80 

60    60 

0.80 

July     2__ 

2 

70    70 

0.85 

0.82 

1.22 

2.43 

1.57     +  0.86 

75    75 

0.80 

70    65 

1.05 

July     2.. 

3 

75    70 

0.90 

0.95 

1.43 

2.12 

1.22     +0.90 

85    75 

0.90 

65    65 

1.00 

July     2.. 

4 

75    70 

0.90 

0.93 

1.50 

2.15 

1.12     +  1.03 

85    80 

0.90 

60    60 

0.80 

July     2._ 

5 

70    70 

0.85 

0.85 

1.32 

2.35 

1.40     +  0.95 

80    80 

0.90 

65    60 

0.85 

July  30.. 

1 

75    70 

0.80 

0.87 

1.39 

2.30 

1.29  !  +  1.01 

80    80 

0.90 

60    60 

0.80 

July  30.. 

2 

65    65 
75    75 

0.70 
0.80 

0.77 

1.32 

2.56 

1.38     +  1.18 

The  Photographic  Rays  of  Light. 


67 


TABLE  XLVI— Continued. 


Polaris. 

Q 

m' 

J    m' 

Date. 

Plate. 

d 

Q 

Polaris. 

a 
Andro. 

Polaris. 

a 
Andro. 

1890. 

75    65 

1.10 

. 

July  30- 

3 

80    75 
85    80 

1.05 
0.90 

1.02 

1.70 

1.96 

0.85     +1.11 

65    65 

1.00 

July  30- 

4 

70    70 

0.85 

0.88 

1.36 

2.28 

1.33 

+  0.95 

75    75 

0.80 

60    60 

0.80 

July  30- 

5 

65    65 

0.70 

0.78 

1.35 

2.54 

1.35 

+  1.19 

75    75 

0.80 

65    70 

1.05 

Aug.    6- 

1 

75    75 

1.00 

1.02 

1.59 

1.96 

1.00 

+0.96 

85    85 

1.00 

65    65 

1.00 

Aug.    6- 

2 

75    70 

0.90            0.97 

1.55 

2.06 

1.05 

+  1.01 

85    85 

1.00 

\f 

65    70 

1.05 

Aug.    6- 

3 

70    70 

0.85 

0.93 

1.55 

2.15 

1.05  1  +  1.10 

80    80 

0.90 

65    65 

1.00 

Aug.    6- 

4 

70    70 

0.85 

0.92 

1.54 

2.18 

1.07 

+  1.11 

80     - 

0.90 

65    65 

1.00 

Aug.    6- 

5 

70    70 

0.85 

0.88 

1.43 

2.28 

1.22 

+  1.06 

75    75 

0.80 

60    60 

0.80 

Aug.  12- 

1 

65    65 

0.70 

0.77 

1.28 

2.57 

1.47 

+  1.10 

75    75 

0.80 

! 

. 

68  Terrestrial  Atmospheric  Absorption  of 


TABLE  XLVI— Continued. 


Polaris. 

Q 

TO' 

A  m' 

Date. 

1890. 
Aug.  12.. 

Plate. 

d 

Q 

Polaris. 

a 
Andro. 

Polaris. 

a; 
Andro. 

2 

60  65 
65  65 
80  80 

0.80 
0.70 
I  0.80 

0.77 

1.29 

2.57 

1.45 

+  1.12 

Aug.  12.. 

3 

65  65 
75  75 
90  85 

1.00 
1.00 
1.05 

1.02 

1.44 

1.96 

1.21 

+  0r75 

Aug.  12- 

4 

65  70 
70  75 
80  85 

1.05 
1.05 
0.90 

1.00 

1.52 

2.00 

1.09 

+  0.91 

Aug.  12- 

5 

60  60 
65  70 
75  80 

0.80 
0.80 
0.80 

0.80 

1.24 

2.48 

1.54 

+  0.94 

Aug.  13.. 

1 

65  70 

75  75 
85  85 

1.05 
1.00 
1.00 

1.02 

1.31 

1.96 

1.41 

+  0.55 

Aug.  13- 

2 

65  65 
75  75 
85  85 

1.00 
1.00 
1.00 

1.00 

1.32 

2.00 

1.39 

+  0.61 

Aug.  13- 

3 

75  75 
85  85 
90  90 

1.45 
1.30 
L15 

1.30 

2.12 

1.43 

0.37 

+  1.06 

Aug.  13- 

4 

65  65 

75  75 
85  80 

1.00  . 
1.00     0.97 
0.90 

1.43 

2.06 

1.22 

+  0.84 

Aug.  13.. 

5 

60  60 
65  70 
75  80 

0.80 
0.80 
0.80 

0.80 

1.23 

2.48 

1.55 

+  0.93 

In  Table  XLVII  the  factor  /  is  given  for  each  plate.  As 
the  several  values  are  consistently  smaller  than  for  the  other 
series,  I  was  for  a  time  at  a  loss  to  account  for  this  difference. 
A  comparison  of  the  negatives  developed  by  W.  W.  C.  with  those 
developed  by  J.  M.  S.  at  once  showed  that  the  latter  films  are 
considerably  darker  than  the  former. 

As  some  of  the  negatives  of  this  third  series  are  darker  than 
others,  the  following  test,  as  to  whether  the  value  of  the  factor 
/  is  a  function  of  the  degree  of  development  of  the  plate,  was 
made:  All  the  plates  of  the  third  series  were  fastened  side  by 
side  to  a  large,  white,  semi-transparent  background  (a  frosted 
Avindow  pane);  thus  arranged,  slight  differences  of  shade  could 
at  once  be  detected.  Only  two  grades  of  density  will  be  used 


The  Photographic  Rays  of  Light. 


69 


to  designate  the  degree  of  opacity,  light  (L)  and  dark  (D); 
the  corresponding  value  of  /  is  found  in  the  horizontal  line. 
It  should  also  be  remarked  that  on  three  of  the  six  nights 
of  observation  the  moon  was  nearly  full,  so  that  a  light 
development  under  such  conditions  would  correspond  to  a 
considerably  lighter  development  on  a  moonless  night,  as  the 
diffused  light  resulting  from  the  presence  of  the  moon  in  the 
sky  would,  to  a  certain  extent,  fog  the  whole  plate. 


TABLE  XLVII. 


Date. 

Plate. 

Develop- 
ment. 

Mean 
Zenith- 
Distance. 

» 

/=! 

REMARKS. 

1890. 

July     1- 

1 

D 

60.5 

1.25 

0.44 

Moon    nearly   full  — 

July     1- 

2 

D 

61.2 

1.20 

0.40 

very  windy. 

July     2- 

1 

L 

68.5 

1.48 

0.37 

Full  moon  — 

July     2- 

2 

L 

67.7 

1.22 

0.40 

very  windy. 

Julv     2.. 

3 

L 

67.1 

1.43 

0.40 

July     2.. 

4 

L 

66.2 

1.50 

0.43 

July    2.. 

5 

L 

65.3 

1.32 

0.36 

July  30.. 
July  30- 

1 

2 

L 
L 

59.3 
53.6 

1.39 
1.32 

0.45 
0.36 

Moon  nearly  full. 

July  30.. 

3 

L 

53.0 

1.70 

0.38 

July  30- 

4 

L 

57.8 

1.36 

0.37 

July  30- 

5 

L 

57.2 

1.35 

0.36 

Aug.    6.. 

1 

D 

67.1 

1.59 

0.47 

Moon  rise  near  close 

Aug.    6- 

2 

D 

66.6 

1.55 

0.41 

of  observations. 

Aug.    6.. 

3 

D 

66.1 

1.55 

0.47 

Aug.    6.. 

4 

D 

65.5 

1.54 

0.43 

Aug.    6_. 

5 

D 

65.3 

1.43 

0.52 

Aug.  12.. 

1 

D 

47.2 

1.28 

0.46 

Aug.  12.. 

2 

D 

47.6 

1.29 

0.41 

Aug.  12- 

3 

D 

53.3 

1.44 

0.51 

Windy. 

Aug.  12- 

4 

D 

52.7 

1.52 

0.44 

Aug.  12- 

5 

D 

44.3 

1.24 

0.63 

Aug.  13.. 

1 

L 

52.7 

1.31 

0.37 

Aug.  13.. 

2 

L 

51.8 

1.32 

0.41 

Aug.  13- 

3 

L 

51.2 

[2.121 

(0.59) 

Aug.  13.. 

4 

L 

50.7 

1  43 

0.41 

Aug.  13- 

5 

D 

50.1 

L23 

0.44 

In  Table  XL VIII  the  mean  results  for  each  day,  together 
with  the  meteorological  factors,  pressure  and  temperature, 
will  be  found  tabulated.  The  variations  in  pressure  and  tem- 
perature are  altogether  too  small  to  enable  one  to  decide  just 
what  effect  the  purely  meteorological  factors  have  upon  the  ab- 


Terrestrial  Atmospheric  Absorption  of 


sorption.  Such  an  effect  can,  however,  probably  be  considered 
as  evanescent  compared  with  the  unknown  errors  arising  from 
other  sources,  as,  for  instance,  impurities  in  the  atmosphere. 

TABLE  XLVIII. 


hsr 

Mean 
Zenith- 
Distance. 

Pressure. 

Temper- 
ature. 

<?o 

f 

July    1                                 D 

60°.  8 

2oin.ll 

63° 

1.22 

0.42 

July    2                           !        L 

70  .0 

25   .07 

63 

1.39 

0.39 

July  30                                 L 

56  .2 

24   .96 

65 

1.42 

0.38 

Aug    6                                 D 

66  .1 

25   .09 

68 

1.53 

046 

Aug.  12                          I         D 

49  .0 

24   .90 

67 

1.34 

0.49 

Aug.  13                1        L 

51  .3 

25   .03 

64 

1.32 

0.41 

It  will  be  noticed  that  values  of  /,  corresponding  to  a  D 
development,  are  all  greater  than  those  for  an  L  development. 
The  D  developments  again  are  all  very  much  less  dense  than 
my  own,  for  which  the  value  of  /  is  about  0.60.  I  therefore 
conclude  that  the  small  value  of  /,  in  the  case  of  a  Andromedae, 
is  to  some  extent  at  least  due  to  the  difference  found  in  the 
developments  of  the  plates.  An  idea  of  the  relative  blackness 
of  the  films,  as  well  as  an  approximation  to  the  absolute  densi- 
ties, can  be  obtained  from  the  following  experiment:  Any  three 
negatives  developed  by  J.  M.  S.,  when  superposed,  form  a  good 
dark  glass  for  viewing  the  sun  without  telescopic  aid,  while  it 
takes  five  of  the  D  negatives,  developed  by  W.  W.  C.,  to  cut  off 
the  same  amount  of  light.  The  LICK  Observatory  has  tem- 
porarily in  its  possession  some  HARVARD  College  Observatory 
plates,  of  which  it  takes  seven  to  make  a  dark  glass  of  the 
same  degree  of  opacity  as  described  above.  (BACHE  telescope 
plates  of  D.  M.  stars.) 

That  the  value  of  the  factor  /  is  to  a  certain  degree  dependent 
upon  the  degree  of  development  seems  to  be  evident  from  the 
following  considerations: 

The  image  of  a  bright  star  grows  more  rapidly  than  does  the 
image  of  a  faint  star.  In  developing,  the  faint  star  will,  after 
its  first  appearance,  increase  but  very  little  in  size;  but  such  is 
not  the  case  for  a  bright  star — the  longer  the  development, 
the  larger,  as  a  rule,  will  be  the  size  of  the  disk.  So  that  for 
a  long  development  the  ratio  of  the  diameters  of  the  images  of 
the  same  star  for  the  two  extremes  of  altitude  will  differ  more 


The  Photographic  Rays  of  Light.  71 

from  unity  than  will  be  the  case  for  a  short  development.  It 
consequently  seems  to  follow  that  the  factor  /  should  theoretic- 
ally be  greater  for  long  developments  than  for  light  develop- 
ments, agreeing  apparently  with  actual  observation. 

Another  cause  which  has  a  tendency  to  diminish  the  value 
of  the  factor  /  is  improper  focal  adjustment  of  the  sensitive 
plate.  It  is  evident  that  if  the  images  are  slightly  out  of  focus, 
the  ratio  of  the  diameters  of  the  images  for  the  extreme  values 
will  differ  less  from  unity  for  the  faulty  focus  than  it  will  for 
the  good  focus;  since  the  ratio  of  the  increase  in  diameter  to 
the  whole  diameter  will  be  much  greater  for  the  smaller  images 
than  it  will  be  for  the  larger,  provided  the  density  or  blackness 
of  the  badly  focused  image  is  sufficiently  great  to  admit  of 
proper  measurement. 

In  the  present  series,  however,  the  focus  seems  to  have  been 
right,  so  that  this  explanation  cannot  be  applied  to  account  for 
the  discrepancy. 

If  we  use  only  those  values  of  /  which  correspond  to  the  D 
developments  of  the  a  Andromedae  plates,  we  have  the  ex- 
pression 

B  =  B0l  —  0.46  <p  (<2)2  (152) 


If  for  determining  the  relative  photographic  magnitudes  of 
tx  Andromedae  in  the  zenith,  and  Polaris  at  the  pole,  we  assign 
equal  weights  to  all  the  observations,  we  have  the  relative 
numbers 

Uncorrected     magnitude    of    Polaris   at   the   pole, 
=  2".21  ....  £=56°  40'.  , 

Uncorrected  magnitude  of  a  Androm.  in  the  zenith,  ' 
=  lm.25  ....  <§  =  0°0'. 

Photographically,  therefore,  a  Andromedae  can  become  nearly 
a  whole  magnitude  brighter  than  Polaris,  as  seen  from  the  LICK 
Observatory,  if  atmospheric  absorption  is  not  allowed  for. 

The  fact  that  the  Uncorrected  magnitude  of  Polaris  comes  out 
2.21  instead  of  2.00,  would  also  seem  to  indicate  that  the  plates 
were  under-developed,  using  my  developments  as  a  standard 
of  reference.  If  a  brighter  star  than  a  Andromedae  had  been 
used,  more  satisfactory  results  would  doubtless  have  been 
obtained,  since  for  a  comparatively  faint  star  the  images  for 


72  Terrestrial  Atmospheric  Absorption  of 

short  exposures  are  small,  and  at  great  zenith-distances  more 
or  less  ill-defined,  so  that  a  very  slight  error  in  the  measures 
produces  a  very  large  error  in  the  deduced  brightness.  If  the 
observations  are  to  be  carried  to  the  horizon,  a  first  magnitude 
star  must  be  selected,  as  no  impression  suitable  for  measure- 
ment can  ordinarily  be  obtained  from  fainter  stars. 

As  has  already  been  stated,  the  photographic  magnitude  2.00 
has  been  given  to  Polaris  at  the  zenith-distance  52°  40'.  At  the 
close  of  this  paper  a  new  unit  of  brightness  will  be  adopted,  in 
which  the  correction  for  the  atmospheric  absorption  of  the 
photographic  rays  will  be  allowed  for  in  such  a  way  that  the 
brightness  1.00  and  the  magnitude  2.00  will  be  assigned  to 
Polaris,  as  it  would  appear  in  the  zenith  of  the  LICK  Obser- 
vatory. 

DISCUSSION    OF    THE    FOURTH    SERIES    OF    OBSERVATIONS    FOR 
ABSORPTION. 

After  I  had  made  a  preliminary  discussion  of  the  several 
series  of  observations  already  recorded  in  the  preceding  pages, 
I  was  very  anxious  to  supplement  these  observations  by  an- 
other series,  to  see  whether  the  law  which  I  had  found  to  rep- 
resent the  observations  to  80°-85°  zenith-distance  would  also 
represent  observed  data  corresponding  to  90°  zenith-distance. 

I  was  all  the  more  impelled  to  make  these  additional  ob- 
servations, as  there  seemed  to  be  some  doubt  as  to  whether  the 
proper  explanation  had  been  given  to  account  for  the  small 
value  of  the  factor  /  in  the  case  of  the  a  Andromedae  results. 

As  the  DALLMEYER  telescope  had  in  the  meantime  been  re- 
turned to  Washington,  it  was  determined  to  use  the  newly 
mounted  CROCKER  telescope,  containing  the  WILLABD  lens  (re- 
figured  by  BRASHEAR)  already  spoken  of. 

This  instrument  is  in  a  building  with  a  revolving  dome. 
The  pointings  are  made  with  a  small  telescope  about  two  feet 
long,  which,  with  the  photographic  telescope,  is  fastened  to  an 
equatorial  mounting  by  BRASHEAR.  In  all  the  previous  ex- 
posures 4x5  SEED  plates  (No.  26)  were  used.  As  the  plate- 
holders  for  the  CROCKER  telescope  were  all  of  the  8  x  10  size, 
SEED  plates  of  the  same  size  were  consequently  used  on  all  the 
exposures  of  this  series. 


The  Photographic  Rays  of  Light. 


As  the  primary  object  of  this  series  was  to  test  the  law  for 
very  great  zenith-distances,  a  star  of  the  first  magnitude  (pho- 
tographic) was  required  to  give  the  most  reliable  results.  For 
various  reasons,  which  need  not  be  considered  here,  a  Lyrae 
seemed  to  be  the  most  suitable  star  available,  although  its 
zenith-distance  at  the  close  of  evening  twilight  was  already 
about "45°;  this,  however,  was  not  considered  to  be  a  serious 
objection,  as  the  law  from  the  zenith  down  to  about  80°  z.-d. 
was  already  known. 

To  determine  the  correction  to  be  applied  to  the  measured 
values  of  d'  in  the  case  of  a  Lyrae,  I  made  a  series  of  exposures 
on  this  star  with  the  CROCKER  telescope.  The  measured 
diameters  of  the  images  are  given  in  the  column  headed  d'  of 
the  following  table. 

According  to  equation  (12),  taken  in  connection  with  that 
of  (14),  the  required  correction  (c — c)  can  now  be  obtained 
from  any  two  values  of  d'  corresponding  to  given  values  of  t. 

For  obvious  reasons,  the  errors  in  the  individual  measures 
will  have  the  least  effect  upon  the  resulting  values  of  (c — c') 
when  the  difference  between  the  two  values  of  d'  is  the  greatest. 
If,  therefore,  we  let  t0=l"  and  t  =  512s,  the  corresponding 
values  of  d'0  and  d'  being  respectively  0.0099  and  0.0395.  the 
equation  (16)  at  once  gives  for  Q  the  value 


0.0296 


0.0033  X  2.709 


(154) 


With  this  value  of  Q  as  an  argument,  we  now  take  from 
Table  II  the  tabular  values  given  in  the  column  headed  d'. 
The  fourth  column  contains  the  individual  values  of  d — d'  = 
c—c'. 

TABLE  XLIX. 


t 

d' 

d 

c—c' 

1» 

0.0099 

0.0071         —0.0028 

2 

0.0132 

0.0104           0.0028 

4 

0.0165 

0.0137           0.0028 

8 

0.0195 

0.0170           0.0025 

16 

0.0225 

0.0203           0.0022 

32 

0.0260 

0.0236           0.0024 

64 

0.0297 

0.0268           U."<>2*.. 

128 

0.0327           0.0301           0.0028 

256 

0.0360           0.0334 

0.0026 

512 

0.0395 

0.0367 

0.0028 

74  Terrestrial  Atmospheric  Absorption  of 

From  the  above  comparisons,  it  will  be  seen  tbat  tbe  agree- 
ment between  theory  and  observation  is  as  close  as  could  be 
expected.  The  quantity  c — c'  is  large,  and  indicates  that  the 
WILLARD  lens  is  much  more  effective  than  the  DALLMEYER.  I 
have,  however,  assumed  this  quantity  to  be  a  constant  for 
a  Lyrae,  as  all  the  other  plates  of  this  series  were  exposed, 
developed,  and  measured  in  the  same  way. 

The  photographic  magnitude  (provisional)  corresponding  to 
Q=  3.3  is,  according  to  Table  II,  TO=  —  0.597,  agreeing  fairly 
well  with  the  magnitude  given  by  the  standard  telescope. 

.  Explanation  of  the  Tables  L-LV. 

The  first  three  columns  need  no  explanation,  as  the  arrange- 
ment is  the  same  as  for  the  preceding  tables.  In  the  fourth 
column,  two  independent  measures  of  the  diameters  of  each 
stellar  image  are  given.  As  the  images  are  slightly  elongated, 
these  measures  were  made  along  two  diameters,  at  right  angles 
to  each  other.  The  fifth  column  gives  the  corrected  mean 
diameter,  found  by  subtracting  0.0027  from  the  mean  of  the 
measured  diameters.  These  two  columns  correspond  to  the 
2s  exposures.  The  same  explanation  applies  to  the  columns 
for  the  4s,  8s,  and  16s  exposures. 

In  forming  the  equations  .of  condition  in  the  previous 
investigations,  I  have  used  the  mean  of  the  results  correspond- 
ing to  the  2s,  4s,  and  8s  exposures. 

In  the  present  case  I  have  treated  each  set  of  exposures 
corresponding  to  the  same  value  of  t  separately,  and  for  two 
reasons:  First,  the  short  exposures  near  the  horizon  will  give 
more  uncertain  results  than  the  longer  exposures,  and  there- 
fore the  least  weight  should  be  given  to  the  2s  exposures,  and 
the  greatest  weight  to  the  16s  exposures;  second,  the  relation 
between  d,  Q,  and  t  may  not  be  exactly  the  same  for  this  tele- 
scope as  that  found  for  the  standard  instrument. 

Any  marked  deviation  from  the  assumed  law,  for  this  instru- 
ment, would  then  become  apparent  through  the  relations,  which 
would  show  that  the  final  results  are  in  each  case  functions  of 
the  time  of  exposure. 


77ie  Photographic  Rays  of  Light. 


75 


Crocker  Telescope.            a  Lyrae.               Bar-.  25>°.92. 

Att..  57°. 

Nov.  4,  1891.                TABLE  L.               Ex  5r 

- 

2*         4*         8* 

16' 

T 

r 

T 

d 

do 

d 

</., 

*  \  * 

d 

do 

0.0 

0.0   0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

2lh42-» 

3"  9» 

37°.2 

125 

98  1  160 

125 

195 

168 

230 

198 

125 

145 

195 

220 

22  13 

3  40 

42  .9 

125 

95   155 

123 

195 

165 

235 

203 

120 

145 

190 

225 

23  13 

4  40 

'•>'-•  .8 

125 

.93 

150 

118 

190 

158 

225 

190 

115 

140 

180 

210 

0  13 

5  40 

64.5 

120 

85 

140 

108 

185 

145 

210 

178 

105 

130 

180 

200 

1   5 

6  32 

7  .0 

110 

75 

130 

95 

170 

133  i  185 

155 

95 

115 

150 

180 

1  34 

7   1 

77.5 

95 

60 

100 

68 

145 

110 

170 

138 

80 

90 

130 

160 

1  48     7  15 

79.5 

90 

60 

100 

68 

145 

108   160 

128 

35 

90 

125 

150 

Equations  of  Condition. 


Values  of  Q  corresponding  to  do. 

a  —  tan  1  (  T^  )    1  ft 

2" 

4s 

, 

16s 

a  —  0.17/3=                      2.80 
a  —  0.22  f^—                       2.60 

2.80 
2.70 

| 
3.15  i 

3.20 
3.30 

(155) 

a  —  0.37/7=                      2.50 

2.50 

2.90 

3.00 

a  —  0.55/7=                        2.00 

2.10 

2.55  i 

2.75 

a  —  0.75  /?=                       1.45 

1.60 

2.20  ! 

2.25 

a  —  0.89/3  = 

0.80 

0.80 

1.60  ' 

1.90 

a  —  0.96/5  = 

0.80 

0.80 

1.55  1 

1.65 

76  Terrestrial  Atmospheric  Absorption  of 

Normal   Equations. 


First  Members. 

Second  Members. 

(156) 

2s 

4s 

8* 

16s 

7.00  a  —  3.91  ft  = 
3.91  a  ~  2.79/3  = 

12.95 
5.64 

13.30 
5.82 

17.10 

8.26 

18.00 

8.85 

Nov.  4,  1891. 


Solution  of  Normals. 

Weight. 
1 


Time. 

OS 

$«  =  3.32 

4s  

'    t/3  =  2.Q3 
U  =  3.38 

8s 

-    ^  =  2.65 
j  a  =  3.64 

16s 

--    (/3  =  2.14 
(a  =  3.68 

"    1/3=1.99 

(157) 
(158) 
(159) 
(160) 


Observation — Computation. 
TABLE  LI. 


2' 

4s 

8* 

16' 

37°.2 

—  0.07                —0.13                —0.08 

—  0.13 

42  .9 
53  .8 
64  .5 
73  .0 
77  .5 

—  0.14                 —0.10 
+  0.15                 +0.10 
+  0.13                 +0.18 
+  0.10                 +0.21 
—  0.22                 —0.22 

—  0.02                 +0.06 
+  0.05                 +0.05 
+  0.08                 +  0.16 
+  0.16                 +0.06 
—  0.14                 —0.01 

79  .5 

0.00 

—  0.04 

—  0.04                 —0.12 

The  Photographic  Rays  of  Light. 


77 


Crocker  Telescope. 
Nov.  6,  189L 


a  Lyrae. 
TABLE  LII. 


Bar.,  25i".84. 
Att.,    46°. 
Ex.,  47°. 


5 

4s 

8s 

16' 

'  T         T 

f 

d 

do 

d 

do 

d 

do 

d  |  do 

\            II 

1!  o.o 

0.0 

0.0 

0.0  |!  0.0 

0.0 

0.0 

0.0 

22»44» 

4"  11»   48°.5   145 

115 

180 

148   200 

170 

235 

208 

i  140 

170 

195 

23  46    5  13 

59  .6  i  140 

108 

165 

135 

190 

155 

220 

193 

135 

160 

175 

0  46 

6  13 

70.5   135 

100 

150 

120 

175 

140 

210 

175 

I  120 

145 

160 

195 

1  49 

7  16 

79  .7  i;  115 

83 

125    95   150 

118 

175 

140 

!  105 

120 

rvrr 

140 

f**v  it   -trte 

160 

2  27 
2  34 
2  42 


7  54 

8  1 
8      9 


85  .2       100 

85 


2   47          8    14 


86  .1 

87  .2 
87.5 


125 

110 

110 
90 

100 
80 

90 

75 


63 


125 
120 


115 
100 


100 
90 


Equations  of  Condition. 


Values  of  Q  corresponding  to  do. 

"    ""LOwl' 

4s 

8* 

16s 

a  -0.29/3= 

4.00 

3.70 

3.30 

3.40 

or  —  0.46/5  = 

3.60 

3.20 

2.85 

3.10 

(161) 

a  —  0.69/5  = 

3.00 

2.60 

2.40 

2.70 

a  —  0.97  /?=f 

1.90 

L60 

L80 

1.90 

a  —  1.21  /5  = 

1.00 

0.80 

L10 

LOO 

a  —  1.26/3  = 

0.70 

0.50 

0.75 

0.75 

a  —  1.32/5=                       0.40 

0.35 

0.60 

0.60 

or  —  1.33/5=                       0.30 

0.30 

0.40 

0.50 

1 

78  Terrestrial  Atmospheric  Absorption  of 


Normal  Equations. 

First  Membe 

Second  Members. 

j    » 

4' 

8*               16* 

(162) 

8.00  a  —  7.53/5=                 14.» 
7.53  a  —  8.27/3=                   9.8 

)           13.05 
L             8.34 

13.20           13.95 
957             9.72 

Solutio 
Time. 

n  of  Normals. 
Weight. 

=  3^56              1 
=  4.76               2 

=  2'.89               8 

m  —  Computation. 
LBLE  LIU.       _ 

(163) 
(164) 
(165) 
(166) 

£ 

16 

Nov.  6,  1891. 

<p  = 

Observati 
T. 

c 

0  C 

2s 

4s                         8* 

16* 

48°.5 
59.6 
70.5 
79  .7 
85.2 
86  .1 
87  .2 
>7  6 

—  0.18 
—  0.02 
+  0.20 
+  0.14 
+  0.10 
+  0.03 
—  0.06 
—  0.18 

—  0.09 
—  0.03 
+  0.14 
+  0.07 
+  0.07 
—  0.06 
—  0.01 
—  0.03 

—  0.09 
-  0.08 
+  0.08 
+  053 
+  0.17 
-0.05 
—  0.04 
—  0.21 

—  053 
+  0.04 
+  052 
+  0.23 
+  0.02 
—  0.09 
—  0.06 
—  0.13 

The  Photographic  Rays  of  Light. 


Crocker  Telescope. 
Nov.  8,  1891. 


a  Lyrae.    ' 
TABLE  LIV. 


Bar.,  26">.03. 
Alt.,  57°. 
Ex.,  58°. 


T 

r 

s 

* 

4 

• 

g 

• 

'  'l 

3« 

d 

do 

d 

do 

d 

do 

d 

do 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

23h  7m 

4h  3401 

52°  6 

125 

93 

145 

113 

115 

135 

1   0 

6'  27 

72  2 

105 

70 

90 

1  40 

7  7 

78  .3 

100 

70 

105 

73 

120 

88 

145 

110 

95 

95 

110 

130 

2  10 

7  37 

82.7 

85 

53 

90 

60 

100 

70 

120 

90 

75 

85 

95 

115 

2  24 

7  51 

84  .7 

75 

43 

80 

50 

90 

60 

65 

75 

85 

2  33 

8  0 

85.9 

70 

38 

75 

43 

80 

48 

•  95 

63 

60 

65 

70 

85 

2  45 

8  12 

87  .5 

55 

25 

60 

33 

70 

40 

75 

48 

50 

60 

65 

75 

2  52 

8  19 

88  .3 

45 

18 

55 

28 

65 

33 

65 

38 

45 

55 

55 

65 

2  57 

8  24 

88  .9 

50 

23 

55 

23 

60 

30 

50 

45 

55 

3  05 

8  27^ 

89  3 

50 

18 

40 

80 


Terrestrial  Atmospheric  Absorption  of 


Equations 

o/  Condition. 

Values  of  Q  corresponding  to  dc 

"  J^i-GOr 

2" 

8-              16 

8 

a  —  0.35/3  = 
a—  0.73^  = 
a  —  0.92/3  = 
a  —  L09/3  = 
a      L19  /3  — 

2.50 
1.20 
L20 
0.60 
0.35 
0.25 
0.10 
0.07 

2.35 

0.95             1.10 
0.60             0.70 
040             050 

1.30 
D.90 
/  -1  e*f'\ 

a  —  1.25/3  = 
a  —  1.33/3  = 
nr  —  1.39/3  = 
a  —  1.42/3  = 
a:      1  45  /3  — 

0.30             0.30 
0.20             0.20 
0.15             0.15 
0.10             0.09 
006 

iCw'   (16° 

D.30 
D.20 
).10 

""  """ 

2s 
4s    .       ._ 

Normal 

(    8.00  a 
j   8.25  a 

$    8.00  a 
(   8.94  a 

$    8.00  a 
1  10.04  a 

1    6.00  a 
i    7.40  a 

/SoZwfion 

Equations. 

—    8.25/5  =  6.27 
—    9.37/5  =  4.46 

—    8.94  y5  =  5.05 
—  10.86  ft  =  3.78 

—  10.04  ft  =  3.10 
—  12.84/5  =  3.44 

—    7.40/5  =  3.35 
—   9.32/5  =  3.69 

o/  Normals. 
Weight. 
J 

3.00 
2.12 

2.68               4 
3.36 

(168) 
(169) 
(170) 
(171) 

(172) 
(173) 
(174) 
(175^ 

8s 

16s  

Time. 

2s 

4s  

(«  = 

8s  .   . 

\ft  = 

(  a  = 

16s.. 

£ 

The  Photographic  Rays  of  Light. 


81 


Xov.  8,  1891. 


Observation — Computation. 
TABLE  LY. 


o—  c 

c 

» 

4s 

* 

16- 

52°  6 

+  014 

+  009 

—  028 

78  .3 

82  .7 

84  7 

+  0.16 
—  0.05 
—  007 

-0.10 
—  0.09 
—  008 

+  0.10 
+  0.03 
0.00 

+  0.03 
+  0.01 

85  .9 
87  .5 
88  .3 
88  9 

—  0.03 
0.00 
+  0.11 

—  0.05 
+  0.02 
+  0.10 
+  0.11 

—  0.08 
—  0.03 
+  0.03 
+  0.02 

—  0.02 
—  0.04 
0.00 
—  0.04 

89  .3 

+  0.05 

To  see  whether  any  definite  relation  exists  between  the 
values  of  a  and  /?,  and  t  (or  /  and  t)  for  this  particular  tele- 
scope, we  find,  by  taking  simple  means,  the  following  figures: 


TABLE  LVI. 


Exposure. 

a 

ft 

/ 

Weight. 

2" 

3.90 

2.83                     0.70 

t 

4 

3.71 

2.70                      0.73                       2 

8 

3.49 

2.21                      0.63                       4 

16 

3.83 

2.38                      0.62 

8 

The  values  of  /  resulting  from  the  shorter  exposures  are,  for 
the  reason  already  given,  less  reliable  than  those  which  cor- 
respond to  the  longer  exposures;  there  is,  however,  an  evident 
tendency  for  /  to  increase  as  the  exposure  time  diminishes.  I 
account  for  this,  at  least  partly,  as  follows:  The  correction 
—  0.0027  has  only  been  deduced  from  observations  on  a  Lyrae, 
which  correspond  to  exposures  of  one  second  and  more.  The 
smallest  image  to  which  this  correction  has  been  applied  and 
found  to  hold  good,  has  the  diameter  0.0099  (see  Table 
XLIX),  while  the  smallest  image  measured  in  the  series  of 
observations  for  absorption  has  a  diameter  of  0.0045,  which, 
however,  was  used  but  once  to  form  a  single  equation  of  con- 
dition, the  other  values  all  being  greater  than  0.0065.  It  is 
evident  that  if  the  constant  grows  sensibly  smaller  as  the 
image  decreases  from  0.0099  to  the  above  values,  the  corrected 
6 


82  Terrestrial.  Atmospheric  Absorption  of 


diameters  for  the  short  exposures  at  great  zenith-distances  will 
be  too  small,  and  consequently  will  have  the  effect  of  making 
the  factor/  (and,  therefore,  also  the  absorption)  greater  than  it 
actually  is.  It  is  quite  probable  that  the  constant  does  grow 
smaller  within  the  above  range,  but  as  I  had  no  accurate 
method  of  testing  the  law  for  extremely  short  exposures,  and 
as  there  are  no  evidences  pointing  to  such  a  conclusion  in 
Table  XLIX,  I  deemed  it  best  to  use  a  constant  correction  for 
all  the  measures.  It  is  of  course  certain  that  there  is  a  limit 
near  which  this  constant  becomes  a  variable,  which  decreases 
in  magnitude  as  the  exposure  time  diminishes.  A  series  of 
exposures  on  Polaris  with  this  same  telescope,  in  February, 
1892,  made  on  a  new  series  of  plates,  gave  the  correction 
—  0.0010  for  all  exposures  from  1s  to  256s  duration,  but  the 
value  of  the  photographic  magnitude  was  not  affected. 

If  we  give  weights  to  these  results,  which  are  proportional  to 
the  exposure  times,  the  value  of  the  factor  /  becomes 

/  =  0.64  (176) 

If  we  take  the  weighted  mean  of  the  separate  results  of  each 
night,  as  found  for  the  2s,  4s,  8s,  and  16'  exposures,  we  have 
the  following  expressions  for  Q;  the  corresponding  values 
of  /==  ^,  and  the  mean  zenith-distances  <?  are  also  tabulated: 

TABLE  LVII. 


Date. 

r 

Q=a  —  fiq>(t) 

f 

1891. 
November  4  

61° 

—  3.60  —  2.16  <?(£) 

0.60 

November  6 

75 

—  4  4(j  —  2  93  <p  (C) 

0.66 

November  8 

81 

—  3  19        9  13  (p  l£\ 

069 

The  nights  on  which  these  observations  were  made  were  not  of 
the  first  class,  either  as  to  clearness  or  steadiness  of  the  atmos- 
phere. It  is  evident  that  for  observations  at  great  zenith- 
distances  a  small  change  in  the  general  transparency  of  the 
air  will  have  a  great  effect  upon  the  resulting  brightness  in  the 
zenith,  found  by  means  of  the  formula  applied  to  data  derived 
from  observations  made  near  the  horizon.  It  will  be  noticed 
that  the  individual  values  of  a  and  $  are  unusually  large  on 
November  6th,  compared  with  those  of  the  other  two  nights. 


The  Photographic  Rays  of  Light.  83 

I  am  inclined  to  attribute  this  difference  rather  to  greater 
sensitiveness  of  the  particular  plate  used  than  to  greater  trans- 
parency of  the  atmosphere.  The  practical  constancy  of  the 
factor  /,  even  for  decided  variations  of  a  and  ft,  gives  evidence 
that  the  empirical  law  here  deduced  represents  the  true  physical 
law  with  a  very  fair  degree  of  accuracy. 

If  we  take  the  mean  of  the  whole  series  of  observations  the 
equation  for  a  Lyrae  takes  the  form 

Q  =  3.73  —  2.53  <?(<?)  (177) 

The  photographic  magnitude  (provisional)  of  ex  Lyrae,  de- 
duced from  exposures  made  at  a  mean  zenith-distance  of  more 
than  70°,  and  reduced  to  the  zenith  by  means  of  the  formula, 
is,  therefore, 

m'=— 0.85  (178) 

If,  for  determining  the  magnitude,  we  reject  the  abnormal 
result  of  November  6th,  and  take  the  mean  of  the  values  for 
November  4th  and  November  8th,  we  have  the  expression 

Q  =3.28  —  2.24  tp  (<?)  (179) 

This  equation  gives  for  a  Lyrae  the  provisional  magnitude 

m'=  —  0.58 

agreeing  closely  with  the  provisional  magnitude  found  by 
means  of  the  standard  instrument,  and  also  with  the  special 
determination  made  with  the  WILLARD  lens. 

The  equation  which  expresses  the  law  of  atmospheric  ab- 
sorption, as  derived  from  all  the  observations  on  a  Lyrae,  is, 
therefore, 

£  =  £0[l—  0.64  ?>  (<?)]'  (180) 

It  is  a  rather  curious  fact  that  the  resulting  mean  value  of 
/  comes  out  such  that  for  «?  =  90°  we  have  Q  =  0.04,  cor- 
responding to  a  loss  of  seven  magnitudes.  If  this  result  could 
be  regarded  as  freed  from  all  sources  of  error,  it  would  at  once 
follow  that  the  difference -between  the  apparent  visual  and 
the  apparent  photographic  magnitudes  of  the  same  star  at 
different  altitudes  is  not  a  constant  quantity;  the  decrease  in 
the  photographic  brightness  being  much  more  rapid  than  that 
of  the  visual  brightness  for  increasing  zenith-distances.  For, 


84  Terrestrial  Atmospheric  Absorption  of 

in  the  horizon  of  the  LICK  Observatory,  the  star  a  Lyrae  is  still 
plainly  visible  to  the  naked  eye;  it  is,  therefore,  among  other 
things,  highly  probable  that  much  the  greater  portion  of  the 
light  which  reaches  the  observer  from  stars  near  the  horizon 
comes  from  the  visual  or  non-actinic  part  of  the  spectrum, 
agreeing,  I  believe,  with  results  obtained  by  other  methods. 

Other  causes  which  unite  to  bring  about  the  peculiar  result 
for  <?  =  90°,  in  the  case  of  a.  Lyrae,  I  believe  to  be  the  following: 

First — For  the  shorter  exposures  the  images  impressed  upon 
the  photographic  plates  are  too  small  and  indefinite  to  afford 
accurate  data  for  measurement  when  the  zenith-distance  is 
nearly  90°. 

Second — The  smaller  images  can  be  considered  as  equivalent 
to  images  of  bright  stars  having  exposure  times  less  than  one 
second;  the  constant  correction  ( — 0.0027)  used  may  not  be 
strictly  accurate  for  the  extreme  measures  here  considered. 

Third — Near  the  horizon  the  images  are  almost  always  very 
unsteady;  so  that  even  those  actinic  rays  which  strike  the 
photographic  plate  do  not  produce*  the  effect  which  would  be 
caused  by  a  similar  set  of  rays  in  a  perfectly  steady  atmos- 
phere. For  short  exposures,  therefore,  the  observed  photo- 
graphic magnitude,  at  great  zenith-distances,  will,  as  a  rule, 
always  come  out  less  than  the  true  photographic  magnitude; 
for  the  same  reason  just  the  opposite  result  might  be  obtained 
from  long  exposures  on  a  bright  star. 

FINAL  RESULTS  BASED  UPON  ALL  THE  OBSERVATIONS. 

In  combining  all  the  observations  discussed  in  the  preceding 
pages,  the  question,  just  what  weight  should  be  assigned  to  each 
series,  depends  mainly  for  its  answer  upon  three  other  questions, 
that  refer  to  causes  which  exercise  a  preponderating  influence 
upon  the  observed  results. 

First — To  what  zenith-distance  have  the  exposures  been 
carried? 

Second — What  were  the  atmospheric  conditions  at  the  times 
the  exposures  were  made? 

Third — How  were  the  plates  developed? 

The  variations  of  d,  for  moderate  zenith-distances,  are  so 
small,  that  no  matter  how  accurate  the  observed  data  may  be, 
the  law  for  great  zenith-distances  could  not  be  deduced  from 


The  Photographic  Rays  of  Light.  85 


such  observations,  as  a  great  number  of  different  functions 
could  be  found  which  would  represent  such  data — for  moderate 
zenith-distances — quite  accurately.  Hence,  other  things  being 
equal,  the  very  greatest  weight  should  be  given  to  those  deter- 
minations which  depend  upon  observations  made  at  the  greatest 
zenith-distances. 

The  question  as  to  how  to  treat  observations  made  under 
unfavorable  atmospheric  conditions  will  depend  almost  entirely 
upon  the  judgment  of  the  observer.  In  any  case  such  observa- 
tions should  be  given  the  smallest  weight. 

Had  the  development  of  the  plates  of  the  third  series  been 
carried  as  far  as  for  the  other  plates  the  observations  on 
a  Andromedae  would  have  been  given  considerable  weight;  but 
the  fact  of  the  persistently  small  value  of  /  points  so  strongly 
to  a  difference  due  either  to  excessive  development  in  one  case, 
or  under-development  in  the  other  case,  that  using  the  first, 
second,  and  fourth  series  as  standards,  the  third  series  must  be 
given  smaller  weight.  The  fact  that  on  three  of  the  six  observ- 
ing nights  the  moon  was  nearly  full  would  also  require  us  to 
diminish  the  weight  of  the  third  series  of  observations. 

The  following  are  the  values  of  /  for  each  series,  together 
with  corresponding  weights  assigned: 

TABLE  LVIII. 


Series. 

f 

Weight. 

First  —  Mt.  Hamilton 

061 

2 

Second  —  Cayenne 

059 

1 

Third—  Mt.  Hamilton  

0.46 

1 

Fourth  —  Mt.  Hamilton 

064 

3 

Taking  the  weighted  mean  of  these  four  values  of  /,  we  have 
finally  the  following  expression  for  the  adopted  value  of  the 
"Atmospheric  Absorption  of  the  Photographic  Rays  of  Light:" 

B  =  B0[l  —  0.60  ?>(<2)J  (181) 

Explanation  of  Table. 

With  the  aid  of  equations  (181)  and  (4)  the  final  tabular 
quantities  given  in  Table  LIX  have  been  computed  directly 
for  each  whole  degree  of  zenith-distance  from  0°  to  90°. 


Terrestrial  Atmospheric  Absorption  of 


The  first  column  gives  the  observed  zenith-distance,  the 
second  column  the  corresponding  brightness,  and  the  third 
column  the  amount  of  absorption,  expressed  in  magnitudes, 
for  the  same  zenith-distance.  The  brightness  in  the  zenith  is 
placed  equal  to  unity. 

TABLE  LIX. 
TERRESTRIAL  ATMOSPHERIC  ABSORPTION. 


Ob- 
served 
Zenith- 
Dis- 
tance. 

Photographic 

Ob- 
served 
Zenith- 
Dis- 
tance. 

Photographic 

Ob- 
served 
Zenith- 
Dis- 
tance. 

Photographic 

Bright- 
ness. 

Absorp- 
tion. 

Bright- 
ness. 

Absorp- 
tion. 

Bright- 
ness. 

Absorp- 
tion. 

B 

M 

B 

M 

B                m 

0 

1.00    , 

0.00 

30° 

0.87 

0.15 

60° 

0.52          0.71 

1 

1.00 

0.00 

31 

0.86 

0.16 

61 

0.50 

0.74 

2 

1.00 

0.00 

32 

0.86 

0.17 

62 

0.49 

0.78 

3 

1.00 

0.00 

33 

0.85 

0.18 

63 

0.47 

0.81 

4 

1.00 

0.00 

34 

0.84 

0.19 

64 

0.46 

0.85 

5 

1.00 

0.00 

35 

0.83 

0.20 

65 

0.44 

0.89 

6 

0.99 

0.01 

36 

0.82 

0.21 

66           0.42 

0.93 

7 

0.99 

0.01 

37      ;     0.81 

*  0.23 

67      i     0.41 

0.98 

8 

0.99 

0.01 

38 

0.80 

0.24 

68 

0.39 

1.03 

9 

0.99 

0.01 

39 

0.79 

0.26 

69 

0.37 

1.07 

10 

0.99 

0.01 

40 

0.78 

0.27 

70 

0.36 

1.12 

11 

0.99 

0.02 

41 

0.77 

0.29 

71 

0.34 

1.18 

12 

0.98 

0.02 

42 

0.76 

0.30 

72 

0.32           1.24 

13 

0.98 

0.02 

43 

0.74 

0.32 

73 

0.30           1.31 

14 

0.97 

0.03 

44 

0.73 

0.34 

74 

0.28           1.39 

15 

0.97 

0.03 

45 

0.72 

0.35 

75 

0.26 

1.45 

16           0.96          0.04 

46 

0.71 

0.37 

76 

0.25 

1.52 

17           0.96 

0.04 

47 

0.70 

0.39 

77 

0.23 

1.62 

18           0.95 

0.05 

48 

0.69 

0.41 

78 

0.21 

1.71 

19 

0.95          0.05 

49 

0.67 

0.43 

79 

0.19 

1.81 

20 

0.94          0.06 

50 

0.66 

0.45 

80 

0.17 

1.93 

21 

0.94          0.07 

51 

0.65 

0.47 

81 

0.15 

2.05 

22 

0.93          0.07 

52 

0.64 

0.49 

82 

0.13 

2.19 

23 

0.93          0.08 

53 

0.62 

0.52 

83 

0.11 

2.36 

24 

0.92 

0.09 

54 

0.61 

0.54 

84 

0.10 

2.54 

25 

0.91          0.10 

55 

0.59 

0.57 

85 

0.08 

2.75 

26 

0.90          0.11 

56 

0.58 

0.59 

86 

0.06 

3.00 

27 

0.90          0.12 

57 

0.56 

0.62 

87 

0.05 

3.30 

28 

0.88          0.13 

58 

0.55 

0.65 

88 

0.03 

3.70 

29 

0.88 

0.14 

59 

0.53 

0.68 

89 

0.02 

4.18 

30 

0.87 

0.15 

60 

0.52 

0.71 

90 

0.01 

4.96 

The  Photographic  Rays  of  Light.  87 


ON  THE  PROBABLE  ERROR  OF  A  PHOTOGRAPHIC  MAGNITUDE. 

If  we  differentiate  equation  (4),  regarding  m'  and  Q  as  vari- 
ables, we  have 

dm'  =  —  2^-  (182) 

The  expression  shows  that  slightly  erroneous  values  of  Q, 
due  to  constant  or  accidental  errors  of  observation,  will  produce 
large  errors  in  the  resulting  values  of  m'  when  Q  is  very  small. 
For  a  given  value  of  t,  the  error  of  m'  varies  nearly  inversely 
as  Q. 

In  general  the  smaller  the  value  of  the  measured  d,  the 
greater  will  be  the  error  of  the  resulting  value  of  m'. 

However,  when  t  is  very  great,  other  sources  of  error  (due  to 
(1)  imperfect  pointing  of  the  telescope,  (2)  change  in  the  dif- 
ferential refraction,  (3)  change  in  atmospheric  absorption,  (4) 
internal  reflections  in  the  photographic  plate,  etc.)  tend  to 
diminish  the  accuracy  of  the  measured  results. 

The  value  of  the  probable  error,  corresponding  to  a  brightness 
in  the  neighborhood  of  that  assigned  to  the  standard  star,  can  be 
obtained  from  the  data  given  in  Table  XL VI.  Using  all  the 
observations  of  this  table.  I  find  that  the  probable  error  of 
an  observed  magnitude,  deduced  from  the  mean  of  any  three 
exposures  of  2s,  4s,  and  8s  duration,  comes  out  somewhat  less 
than  one  tenth  of  a  magnitude. 

NEW  UNITS  OF  BRIGHTNESS  AND  MAGNITUDE. 

In  the  preceding  discussion,  Polaris  has  been  given  the 
photographic  brightness  1.00,  and  magnitude  2.00,  at  the 
zenith-distance  52°  40'.  From  Table  LIX  we  learn  that  the 
corresponding  brightness  and  magnitude  of  the  same  star,  if 
it  were  situated  in  the  zenith,  would  be  B  =  1.59,  and  m  =1.49. 
Consequently^  if  we  change  this  unit  of  brightness,  so  as  to 
make  it  1.00  in  the  zenith,  we  have  only  to  proceed  in  the  way 
already  outlined  on  page  11,  and  in  equations  (29),  (30),  and 
(31)  to  obtain  the  new  arguments  given  for  Table  II,  found  at 
the  bottom  of  the  page. 

There  seems  to  be  no  marked  change  in  the  law  for  increas- 
ing altitudes  of  the  observer,  if  the  Cayenne  results  can  be 


88  Terrestrial  Atmospheric  Absorption  of 

taken  as  a  test.  Just  what  the  absolute  atmospheric  absorp- 
tion is  in  the  zenith  is  not  known,  nor  is  this  a  necessary 
datum  for  the  purposes  of  this  paper,  as  the  law  has  been  so 
determined  that  only  the  observed  brightness  enters  into  the 
discussion. 

In  Table  LX  will  be  found  the  final  photographic  magnitudes 
of  the  stars  mentioned  in  this  memoir,  as  determined  from  the 
observations. 

TABLE  LX. 


Star. 

Place  of 
Observation. 

Provisional            Final 
Photographic  Photographic 
Magnitude        Magnitude 
(Observed),    j    (Observed). 

i 

aArietis [  Mt.  Hamilton...  +2.10  +2.61 

a  Andromedae I  Mt.  Hamilton... I  +1.04  +1.55 

aOrionis j  Cayenne  ... |  (+1.30)  (+1.81) 

ft  Orionis |  Cayenne j  (—0.64)  (—0.13) 

c  c  Canis  Majoris  ..'... -  -  - :  Cayenne i  (—1.45)  (—  0.94) 

a  Canis  Minoris !  Cayenne j  (+0.10)  (+  0.51) 

a  Lyrae Mt.  Hamilton...!  — 0.59  — 0.08 

Polaris ...:  Cayenne j  (+1.52)  (+2.03) 


The  bracketed  figures  in  the  above  table  indicate  that  the 
values  may  be  considerably  in  error,  as  no  impressions  of  the 
standard  star  that  were  worthy  of  being  used  could  be  obtained 
at  Cayenne;  the  zenith-distance  of  Polaris,  even  at  upper  cul- 
mination, being  greater  than  83°. 

CONCLUSION. 

In  the  practical  application  of  the  finally  adopted  values  of 
the  absorption  at  different  zenith-distances,  the  character  of 
the  particular  kind  of  plate  used  and  the  spectral  type  of  the 
star  observed  must  be  taken  into  consideration. 

A  plate  exposed  to  the  action  of  two  different  sources  of 
light  of  equal  intensity  (visually),  but  coming  from  different 
parts  of  the  spectrum,  Avill  not,  as  a  rule,  be  affected  in  the 
same  way,  for  equal  exposure  times,  by  these  two  lights.  Con- 
sequently, the  law  of  absorption  of  the  photographic  rays,  as 
determined  with  a  particular  kind  of  plate,  may  be  different  for 
stars  having  different  types  of  spectrum. 


Photographic  Rays  of  Light.  89 


As  some  kinds  of  plates  are  more  sensitive  to  a  particular 
part  of  the  spectrum  than  others,  it  follows  that  the  character 
of  the  plate  may  largely  influence  the  final  result  obtained  for 
absorption. 

When  we  take  into  consideration  the  fact  that  the  rays  from 
the  blue  end  of  the  spectrum  appear  to  be  more  absorbed  near 
the  horizon  than  the  rays  from  the  red  end,  the  force  of  the 
above  remarks  becomes  still  more  apparent. 

The  results  given  in  this  paper  are  derived  from  exposures 
made  on  SEED  plates,  Sensitometer  No.  26,  of  their  scale,  and 
should  represent  the  actual  conditions  for  a  normal  state  of 
the  atmosphere.  For  an  unusually  thick  sky,  suitable  for 
observations  of  a  certain  class,  it  is  probable  that  the  value  of 
the  factor  /  is  greater  than  0.60;  while  for  an  unusually  clear 
sky,  its  value  may  be  somewhat  less  than  the  normal  value 
given.  It  is,  of  course,  evident  that  within  a  few  degrees  of 
the  horizon  considerable  uncertainty  will  always  exist  in  all 
measured  data,  and  consequently  also  in  the  computed  theo- 
retical results. 

MOUNT  HAMILTON,  October,  1892. 
7 


WORKS  ISSUED  BY  THE  LICK  OBSERVATORY. 


***  I*  is  intended  to  issue,  at  irregular  intervals,  two  series  of  works,  the  first, 
in  quarto,  to  be  known  as  Publications  of  the  Lick  Observatory;  the  second,  in 
octavo,  to  be  known  as  Contributions  from  the  Lick  Observatory.  Occasional 
pamphlets,  such  as  No.  2  below,  may  not  be  included  in  either  series.  At  the 
end  of  every  book  a  list  of  all  the  works  issued  will  be  given,  for  the  con- 
venience of  librarians  and  others. 

For  the  sake  of  uniformity,  Nos.  3  and  4  below  will  be  counted  as  Contribu- 
tions Nos.  1  and  2. 

1.  Publications  of  the  Lick  Observatory  of  the  University  of  California,  pre- 

pared under  the  direction  of  the  Lick  Trustees  by  EDWARD  S.  HOLDER. 
Volume  1, 1887.  Sacramento,  1887.  4to.  [Containing  a  brief  history  of  the 
Observatory,  with  descriptions  of  the  buildings  and  instruments;  observa- 
tions of  double  stars  by  S.  "NV.  BUBNHAM,  1879,  of  the  transit  of  Mercury, 

1881,  by  Messrs.  FLOYD,  HOLDEX,  and  BURNHAM,  of  the  transit  of  Venus, 

1882,  by  D.  P.  TODD;  meteorological  observations,  by  T.  E.  FRASBH,  1880-85; 
and  Reduction  Tables  for  Mt.  Hamilton,  by  G.  C.  COMSTOCK.] 

2.  Suggestions  for  Observing  the  Total  Eclipse  of  the  Sun  on  January  1, 1889, 

by  EDWARD  S.  HOLDEN.  Printed  by  authority  of  the  Regents  of  the  Uni- 
versity of  California.  Sacramento,  1888.  8vo.  [Out  of  print.] 

3.  Contributions  from  the  Lick  Observatory,  No.  1.    Reports  on  the  Observa- 

tions of  the  Total  Eclipse  of  the  Sun  of  January  1, 1889,  published  by  the 
Lick  Observatory.  Printed  by  authority  of  the  Regents  of  the  University 
of  California.  Sacramento,  1889.  8vo.  [Out  of  print.] 

4.  Contributions  from  the  Lick  Observatory,  No.  2.    Reports  on  the  Observa- 

tions of  the  Total  Eclipse  of  the  Sun,  December  21-22,  1889,  and  of  the 
Total  Eclipse  of  the  Moon,  July  22,  1888,  to  which  is  added  a  Catalogue  of 
the  Library,  published  by  the  Lick  Observatory.  Printed  by  authority  of 
the  Regents  of  the  University  ©^California.  Sacramento,  1891.  8vo.  [Out 
of  print.] 

5.  Contributions  from  the  Lick  Observatory,  No.  3.    Terrestrial  Atmospheric 

Absorption  of  the  Photographic  Rays  of  Light,  by  J.  M.  SCHAEBERLE, 
Astronomer  in  the  Lick  Observatory.  Printed  by  authority  of  the  Re- 
gents of  the  University  of  California.  Sacramento,  1893.  8vo. 

6.  Publications  of   the  Lick  Observatory  of   the  University  of    California. 

Printed  by  authority  of  the  Regents  of  the  University.  Volume  II,  1893. 
Sacramento,  1893.  4to.  [Containing  double  star  observations  made  with 
the  thirty-six-inch  and  twelve-inch  refractors  of  the  Lick  Observatory 
from  August,  1888,  to  June,  1892,  by  S.  W.  BURNHAM.] 

(90) 


Date  Due 


CAT.   NO.   24    161  (**f 


970  00178  3270 


